Pub Date : 2025-12-03DOI: 10.1016/j.physd.2025.135064
Maria Aguareles , Francesc Font
We present a 3D mathematical model for contaminant capture in an adsorption column. The novelty of our approach involves the description of mass transfer by adsorption via a nonlinear evolution equation on the porous media surface, while Stokes flow and an advection-diffusion equation model contaminant transport through the interstices. Simulations with varying microstructures but identical porosity show minimal microstructure impact on contaminant distribution, especially in the radial direction. Using homogenization theory and a periodic microstructure, we derive a 1D adsorption model with two effective coefficients, dispersion and permeability, that explicitly incorporate microstructural details. The 1D model closely reproduces 3D results, including concentration profiles and outlet breakthrough curves. The 3D simulations converge to the 1D model as the microstructure is refined. Our model provides a theoretical foundation for the widely used 1D model, confirming its reliability for investigating, optimising, and designing column adsorption processes.
{"title":"Assessment of averaged 1D models for column adsorption with 3D computational experiments","authors":"Maria Aguareles , Francesc Font","doi":"10.1016/j.physd.2025.135064","DOIUrl":"10.1016/j.physd.2025.135064","url":null,"abstract":"<div><div>We present a 3D mathematical model for contaminant capture in an adsorption column. The novelty of our approach involves the description of mass transfer by adsorption via a nonlinear evolution equation on the porous media surface, while Stokes flow and an advection-diffusion equation model contaminant transport through the interstices. Simulations with varying microstructures but identical porosity show minimal microstructure impact on contaminant distribution, especially in the radial direction. Using homogenization theory and a periodic microstructure, we derive a 1D adsorption model with two effective coefficients, dispersion and permeability, that explicitly incorporate microstructural details. The 1D model closely reproduces 3D results, including concentration profiles and outlet breakthrough curves. The 3D simulations converge to the 1D model as the microstructure is refined. Our model provides a theoretical foundation for the widely used 1D model, confirming its reliability for investigating, optimising, and designing column adsorption processes.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135064"},"PeriodicalIF":2.9,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-02DOI: 10.1016/j.physd.2025.135061
A. Yu Orlov
We consider series over Young diagrams of products of Schur functions sλ ∪ λ, marked with “fat partitions” λ ∪ λ, which appear in matrix models associated with ensembles of symplectic and orthogonal matrices and quaternion Ginibre ensembles. We consider mixed matrix models that also contain complex Ginibre ensembles labeled by graphs and the three ensembles mentioned above. Cases are identified when a series of perturbations in coupling constants turn out to be tau functions of the DKP hierarchy introduced by the Kyoto school. This topic relates matrix models to random partitions - discrete symplectic ensemble and its modifications.
{"title":"Coupling of different solvable ensembles of random matrices II. Series over fat partitions: matrix models and discrete ensembles","authors":"A. Yu Orlov","doi":"10.1016/j.physd.2025.135061","DOIUrl":"10.1016/j.physd.2025.135061","url":null,"abstract":"<div><div>We consider series over Young diagrams of products of Schur functions <em>s</em><sub><em>λ</em> ∪ <em>λ</em></sub>, marked with “fat partitions” <em>λ</em> ∪ <em>λ</em>, which appear in matrix models associated with ensembles of symplectic and orthogonal matrices and quaternion Ginibre ensembles. We consider mixed matrix models that also contain complex Ginibre ensembles labeled by graphs and the three ensembles mentioned above. Cases are identified when a series of perturbations in coupling constants turn out to be tau functions of the DKP hierarchy introduced by the Kyoto school. This topic relates matrix models to random partitions - discrete symplectic ensemble and its modifications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135061"},"PeriodicalIF":2.9,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-02DOI: 10.1016/j.physd.2025.135060
Qinwei Huang, Juan Huang
This paper focuses on a model with homogeneous cubic nonlinearity, which can be derived from classical shallow water theory as an asymptotic model. It is known as the mCH-Novikov equation, as it combines the integrable modified Camassa-Holm (mCH) equation and the Novikov equation. We systematically characterize the point spectrum of the peakon solutions and aim to prove spectral and linear instability on of peakons. To this end, we extend the corresponding linearized operator from to the larger space , since unstable eigenfunctions may reside in , and provides the natural framework for spectral instability analysis. Subsequently, we numerically verify these theoretical findings through spectral stability analysis and time-stepping numerical simulations of the model across different parameter regimes. Specifically, we analyze the parametric dependence of spectral stability to investigate how the mCH and Novikov terms affect the dynamics of the evolution equations.
{"title":"Spectral instability of peakons for a class of cubic quasilinear shallow-water equations","authors":"Qinwei Huang, Juan Huang","doi":"10.1016/j.physd.2025.135060","DOIUrl":"10.1016/j.physd.2025.135060","url":null,"abstract":"<div><div>This paper focuses on a model with homogeneous cubic nonlinearity, which can be derived from classical shallow water theory as an asymptotic model. It is known as the mCH-Novikov equation, as it combines the integrable modified Camassa-Holm (mCH) equation and the Novikov equation. We systematically characterize the point spectrum of the peakon solutions and aim to prove spectral and linear instability on <span><math><mrow><msup><mi>L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> of peakons. To this end, we extend the corresponding linearized operator from <span><math><mrow><msup><mi>H</mi><mn>1</mn></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> to the larger space <span><math><mrow><msup><mi>L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, since unstable eigenfunctions may reside in <span><math><mrow><msup><mi>L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>∖</mo><msup><mi>H</mi><mn>1</mn></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, and <span><math><mrow><msup><mi>L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> provides the natural framework for spectral instability analysis. Subsequently, we numerically verify these theoretical findings through spectral stability analysis and time-stepping numerical simulations of the model across different parameter regimes. Specifically, we analyze the parametric dependence of spectral stability to investigate how the mCH and Novikov terms affect the dynamics of the evolution equations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135060"},"PeriodicalIF":2.9,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-02DOI: 10.1016/j.physd.2025.135063
Cui-Cui Ding , Qin Zhou , B.A. Malomed
We report analytical solutions for diverse multi-pole (MP) soliton and breather states in spatially inhomogeneous binary Bose-Einstein condensates (BECs) with the helicoidally shaped spin-orbit coupling (SOC), including MP stripe solitons on zero background, MP beating stripe solitons on a nonzero plane-wave background, as well as MP beating stripe solitons and MP breathers on periodic backgrounds. The results indicate that modulation effects produced by the helicoidal SOC not only induce stripe patterns in MP solitons, but also generate the spatially-periodic background for the MP beating stripe solitons and breathers. An asymptotic analysis reveals curved trajectories with a logarithmically increasing soliton/breather separation for these MP excitations, fundamentally distinguishing them from periodic trajectories of bound-state solitons/breathers or straight trajectories of conventional multi-soliton/breather sets. With complex periodic structures in individual components, the total density distribution is nonperiodic, due to their configurations which are out-of-phase with respect to the two components. We further examine several degenerate structures of MP solitons and breathers under varying SOC and spectral parameters. Numerical simulations validate the analytical results and demonstrate stability of these MP excitations. These findings may facilitate deeper understanding of soliton/breather interactions beyond conventional multi-soliton systems and bound-state complexes in SOC BEC.
{"title":"Multi-pole solitons and breathers with spatially periodic modulation induced by the helicoidal spin-orbit coupling","authors":"Cui-Cui Ding , Qin Zhou , B.A. Malomed","doi":"10.1016/j.physd.2025.135063","DOIUrl":"10.1016/j.physd.2025.135063","url":null,"abstract":"<div><div>We report analytical solutions for diverse multi-pole (MP) soliton and breather states in spatially inhomogeneous binary Bose-Einstein condensates (BECs) with the helicoidally shaped spin-orbit coupling (SOC), including MP stripe solitons on zero background, MP beating stripe solitons on a nonzero plane-wave background, as well as MP beating stripe solitons and MP breathers on periodic backgrounds. The results indicate that modulation effects produced by the helicoidal SOC not only induce stripe patterns in MP solitons, but also generate the spatially-periodic background for the MP beating stripe solitons and breathers. An asymptotic analysis reveals curved trajectories with a logarithmically increasing soliton/breather separation for these MP excitations, fundamentally distinguishing them from periodic trajectories of bound-state solitons/breathers or straight trajectories of conventional multi-soliton/breather sets. With complex periodic structures in individual components, the total density distribution is nonperiodic, due to their configurations which are out-of-phase with respect to the two components. We further examine several degenerate structures of MP solitons and breathers under varying SOC and spectral parameters. Numerical simulations validate the analytical results and demonstrate stability of these MP excitations. These findings may facilitate deeper understanding of soliton/breather interactions beyond conventional multi-soliton systems and bound-state complexes in SOC BEC.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135063"},"PeriodicalIF":2.9,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01DOI: 10.1016/j.physd.2025.135062
Younghwan Cho , Richard Sowers
Koopman operator theory has been widely applied to data assimilation problems of real systems governed by dynamics, as the theory allows for data-driven construction of modes of dynamical systems. In many modern problems, these modes often must be learned from data with irregular sampling intervals, as opposed to commonly used regularly sampled data. Here, we propose a framework to recover a Koopman eigenfunction–eigenvalue pair for irregularly sampled data. We show that a Koopman eigenpair can be recovered via a natural optimization problem. We provide technical remarks on the anticipated challenges in optimization and suggest a procedure to address them. Simulation studies under different irregular sampling scenarios verify the robustness of the proposed method in learning Koopman eigenfunctions. Compared with extended dynamic mode decomposition on data resampled via interpolation, our method shows improved eigenfunction–recovery accuracy.
{"title":"Koopman representations with irregular time intervals","authors":"Younghwan Cho , Richard Sowers","doi":"10.1016/j.physd.2025.135062","DOIUrl":"10.1016/j.physd.2025.135062","url":null,"abstract":"<div><div>Koopman operator theory has been widely applied to data assimilation problems of real systems governed by dynamics, as the theory allows for data-driven construction of modes of dynamical systems. In many modern problems, these modes often must be learned from data with irregular sampling intervals, as opposed to commonly used regularly sampled data. Here, we propose a framework to recover a Koopman eigenfunction–eigenvalue pair for irregularly sampled data. We show that a Koopman eigenpair can be recovered via a natural optimization problem. We provide technical remarks on the anticipated challenges in optimization and suggest a procedure to address them. Simulation studies under different irregular sampling scenarios verify the robustness of the proposed method in learning Koopman eigenfunctions. Compared with extended dynamic mode decomposition on data resampled via interpolation, our method shows improved eigenfunction–recovery accuracy.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135062"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-29DOI: 10.1016/j.physd.2025.135019
Dock Staal, Arjen Doelman
Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to tipping: a catastrophic process in which a system, driven by gradually changing external factors, abruptly transitions (or collapses) from a preferred state to a less desirable one. In ecosystems, the emergence of spatial patterns has traditionally been interpreted as a possible early warning signal for tipping. More recently, however, pattern formation has been proposed to serve a fundamentally different role: as a mechanism through which an (eco)system may evade tipping by forming stable patterns that persist beyond the tipping point.
Mathematically, tipping is typically associated with a saddle–node bifurcation, while pattern formation is normally driven by a Turing bifurcation. Therefore, we study the co-dimension 2 Turing-fold bifurcation and investigate the question: When can patterns initiated by the Turing bifurcation enable a system to evade tipping?
We develop our approach for a class of phase-field models and subsequently apply it to -component reaction–diffusion systems – a class of PDEs often used in ecosystem modeling. We demonstrate that a two-component system of modulation equations governs pattern formation near a Turing-fold bifurcation, and that tipping will be evaded when a critical parameter, , is positive. We derive explicit expressions for , allowing one to determine whether a given system may evade tipping. Moreover, we show numerically that this system exhibits rich behavior, ranging from stable, stationary, spatially quasi-periodic patterns to irregular, spatio-temporal, chaos-like dynamics.
{"title":"The evasion of tipping: Pattern formation near a Turing-fold bifurcation","authors":"Dock Staal, Arjen Doelman","doi":"10.1016/j.physd.2025.135019","DOIUrl":"10.1016/j.physd.2025.135019","url":null,"abstract":"<div><div>Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to <em>tipping</em>: a <em>catastrophic process</em> in which a system, driven by gradually changing external factors, abruptly transitions (or <em>collapses</em>) from a preferred state to a less desirable one. In ecosystems, the emergence of spatial patterns has traditionally been interpreted as a possible <em>early warning signal</em> for tipping. More recently, however, pattern formation has been proposed to serve a fundamentally different role: as a mechanism through which an (eco)system may <em>evade tipping</em> by forming stable patterns that persist beyond the tipping point.</div><div>Mathematically, tipping is typically associated with a saddle–node bifurcation, while pattern formation is normally driven by a Turing bifurcation. Therefore, we study the co-dimension 2 Turing-fold bifurcation and investigate the question: <em>When can patterns initiated by the Turing bifurcation enable a system to evade tipping?</em></div><div>We develop our approach for a class of phase-field models and subsequently apply it to <span><math><mi>n</mi></math></span>-component reaction–diffusion systems – a class of PDEs often used in ecosystem modeling. We demonstrate that a two-component system of modulation equations governs pattern formation near a Turing-fold bifurcation, and that tipping will be evaded when a critical parameter, <span><math><mi>β</mi></math></span>, is positive. We derive explicit expressions for <span><math><mi>β</mi></math></span>, allowing one to determine whether a given system may evade tipping. Moreover, we show numerically that this system exhibits rich behavior, ranging from stable, stationary, spatially quasi-periodic patterns to irregular, spatio-temporal, chaos-like dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135019"},"PeriodicalIF":2.9,"publicationDate":"2025-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.physd.2025.135054
Yuxuan Li, Tanlin Li, Lin Huang
Using the inverse scattering transform, exact N-soliton solutions are derived for the coupled Yajima-Oikawa system subject to vanishing boundary conditions. Beginning with the newly presented Lax pair, the corresponding Jost functions are constructed and their symmetry and analyticity properties are analyzed. Integral equations for the eigenfunctions lead to the formulation of the Gel’fand-Levitan-Marchenko equations; solving these relations establishes a direct correspondence between the kernel functions and the potential, yielding the general N-soliton expressions. Finally, by appropriate parameter choice, the structural features of the N-soliton solutions are illustrated via graphical plots.
{"title":"Inverse scattering transform for the coupled Yajima-Oikawa systems","authors":"Yuxuan Li, Tanlin Li, Lin Huang","doi":"10.1016/j.physd.2025.135054","DOIUrl":"10.1016/j.physd.2025.135054","url":null,"abstract":"<div><div>Using the inverse scattering transform, exact <em>N</em>-soliton solutions are derived for the coupled Yajima-Oikawa system subject to vanishing boundary conditions. Beginning with the newly presented Lax pair, the corresponding Jost functions are constructed and their symmetry and analyticity properties are analyzed. Integral equations for the eigenfunctions lead to the formulation of the Gel’fand-Levitan-Marchenko equations; solving these relations establishes a direct correspondence between the kernel functions and the potential, yielding the general <em>N</em>-soliton expressions. Finally, by appropriate parameter choice, the structural features of the <em>N</em>-soliton solutions are illustrated via graphical plots.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135054"},"PeriodicalIF":2.9,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145652029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-26DOI: 10.1016/j.physd.2025.135029
Yuan Cai , Xiufang Cui , Fei Jiang , Hao Liu
The small Alfvén number (denoted by ) limit (one type of large parameter limits, i.e. singular limits) in magnetohydrodynamic (abbr. MHD) equations was first proposed by Klainerman–Majda in (Comm. Pure Appl. Math. 34: 481–524, 1981). Recently Ju–Wang–Xu mathematically verified that the local-in-time solutions of three-dimensional (abbr. 3D) ideal (i.e. the absence of the dissipative terms) incompressible MHD equations with general initial data in (i.e. a spatially periodic domain) tend to a solution of 2D ideal MHD equations in the distribution sense as by Schochet’s fast averaging method in (J. Differential Equations, 114: 476–512, 1994). In this paper, we revisit the small Alfvén number limit in with , 3, and develop another approach, motivated by Cai–Lei’s energy method in (Arch. Ration. Mech. Anal. 228: 969–993, 2018), to establish a new conclusion that the global-in-time solutions of incompressible MHD equations (including the viscous resistive case) with general initial data converge to zero as for any given time–space variable with . In addition, we find that the large perturbation solutions and vanishing phenomenon of the nonlinear interactions also exist in the viscous resistive MHD equations for small Alfvén numbers, and thus extend Bardos et al.’s results of the ideal MHD equations in Bardos et al. (1988).
磁流体动力学（简称MHD）方程中的小alfv数极限（用* * *表示）（一种大参数极限，即奇异极限）是由Klainerman-Majda在《Comm. Pure application》中首次提出的。数学。34:481-524,1981)。最近，juwang - xu用Schochet快速平均法在数学上验证了具有一般初始数据在T3（即空间周期域）的三维理想（即不存在耗散项）不可压缩MHD方程的局域解趋向于分布意义上的二维理想MHD方程的解（J.微分方程，14:476-512,1994）。在本文中，我们重新审视了n= 2,3的Rn中的小alfvsamn数极限，并开发了另一种方法，该方法的动机是蔡磊的能量法。配给。动力机械。对于任意给定的时空变量（x,t），当t>；0时，建立了具有一般初始数据的不可压缩MHD方程（包括粘滞阻力情况）的全局时解收敛于0的新结论。此外，我们发现小alfv数的粘阻MHD方程也存在非线性相互作用的大摄动解和消失现象，从而推广了Bardos et al.（1988）中Bardos et al.关于理想MHD方程的结果。
{"title":"Small Alfvén number limit for the global-in-time solutions of incompressible MHD equations with general initial data","authors":"Yuan Cai , Xiufang Cui , Fei Jiang , Hao Liu","doi":"10.1016/j.physd.2025.135029","DOIUrl":"10.1016/j.physd.2025.135029","url":null,"abstract":"<div><div>The small Alfvén number (denoted by <span><math><mi>ɛ</mi></math></span>) limit (one type of large parameter limits, i.e. singular limits) in magnetohydrodynamic (abbr. MHD) equations was first proposed by Klainerman–Majda in (Comm. Pure Appl. Math. 34: 481–524, 1981). Recently Ju–Wang–Xu mathematically verified that the <em>local-in-time</em> solutions of three-dimensional (abbr. 3D) ideal (i.e. the absence of the dissipative terms) incompressible MHD equations with general initial data in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> (i.e. a spatially periodic domain) tend to a solution of 2D ideal MHD equations in the distribution sense as <span><math><mrow><mi>ɛ</mi><mo>→</mo><mn>0</mn></mrow></math></span> by Schochet’s fast averaging method in (J. Differential Equations, 114: 476–512, 1994). In this paper, we revisit the small Alfvén number limit in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math></span>, 3, and develop another approach, motivated by Cai–Lei’s energy method in (Arch. Ration. Mech. Anal. 228: 969–993, 2018), to establish a new conclusion that the <em>global-in-time</em> solutions of incompressible MHD equations (including the viscous resistive case) with general initial data converge to zero as <span><math><mrow><mi>ɛ</mi><mo>→</mo><mn>0</mn></mrow></math></span> for any given time–space variable <span><math><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math></span> with <span><math><mrow><mi>t</mi><mo>></mo><mn>0</mn></mrow></math></span>. In addition, we find that the large perturbation solutions and vanishing phenomenon of the nonlinear interactions also exist in the <em>viscous resistive</em> MHD equations for small Alfvén numbers, and thus extend Bardos et al.’s results of the <em>ideal</em> MHD equations in Bardos et al. (1988).</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135029"},"PeriodicalIF":2.9,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The nonlinear Schrödinger equation (NLSE) is used to study the dynamics of electrostatic wave envelopes in a multi-ion, superthermal plasma. The plasma contains Sr, Ti, and O ions with a -distribution of electrons. We use weakly nonlinear analysis to develop analytical formulas for the dispersion () and nonlinear () coefficients, methodically investigating their effect on the superthermality index and ion concentration ratio We found that reducing (stronger suprathermal effects) increases anomalous dispersion () and self-focusing nonlinearity (), whereas increasing increases modulational instability () via increasing ion inertia and charge density. Localized wave structures are predicted universally by . The Peregrine soliton (transient rogue wave) and Akhmediev breather (periodic modulation) show remarkable spatiotemporal localization in NLSE numerical solutions. Plasma density variations cause mechanical strains beyond material cohesion limitations, causing nanoscale surface deformation under ion irradiation. Our results provide a plasma parameter-based paradigm for nanostructure morphology control in plasma-assisted nanofabrication and space plasma settings.
{"title":"Peregrine soliton and Akhmediev Breather in superthermal multi-ion plasmas and their role in ion-induced nanostructuring","authors":"N.A. El-Bedwehy , R. Sabry , W.M. Moslem , I.S. Elkamash","doi":"10.1016/j.physd.2025.135027","DOIUrl":"10.1016/j.physd.2025.135027","url":null,"abstract":"<div><div>The nonlinear Schrödinger equation (NLSE) is used to study the dynamics of electrostatic wave envelopes in a multi-ion, superthermal plasma. The plasma contains Sr<span><math><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></math></span>, Ti<span><math><msup><mrow></mrow><mrow><mn>4</mn><mo>+</mo></mrow></msup></math></span>, and O<span><math><msup><mrow></mrow><mrow><mn>2</mn><mo>−</mo></mrow></msup></math></span> ions with a <span><math><mi>κ</mi></math></span>-distribution of electrons. We use weakly nonlinear analysis to develop analytical formulas for the dispersion (<span><math><mi>P</mi></math></span>) and nonlinear (<span><math><mi>Q</mi></math></span>) coefficients, methodically investigating their effect on the superthermality index <span><math><mi>κ</mi></math></span> and ion concentration ratio <span><math><mrow><mi>β</mi><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>T</mi><mn>0</mn></mrow></msub><mo>/</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow></msub></mrow></math></span> We found that reducing <span><math><mi>κ</mi></math></span> (stronger suprathermal effects) increases anomalous dispersion (<span><math><mrow><mi>P</mi><mo><</mo><mn>0</mn></mrow></math></span>) and self-focusing nonlinearity (<span><math><mrow><mi>Q</mi><mo><</mo><mn>0</mn></mrow></math></span>), whereas increasing <span><math><mi>β</mi></math></span> increases modulational instability (<span><math><mrow><mi>P</mi><mi>Q</mi><mo>></mo><mn>0</mn></mrow></math></span>) via increasing ion inertia and charge density. Localized wave structures are predicted universally by <span><math><mrow><mi>P</mi><mi>Q</mi></mrow></math></span>. The Peregrine soliton (transient rogue wave) and Akhmediev breather (periodic modulation) show remarkable spatiotemporal localization in NLSE numerical solutions. Plasma density variations cause mechanical strains beyond material cohesion limitations, causing nanoscale surface deformation under ion irradiation. Our results provide a plasma parameter-based paradigm for nanostructure morphology control in plasma-assisted nanofabrication and space plasma settings.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135027"},"PeriodicalIF":2.9,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-25DOI: 10.1016/j.physd.2025.135053
Wenhao Liu, Yufeng Zhang, Zhenbo Wang
In this paper, we apply Riemann-Hilbert approach and steepest descent method to study the Cauchy problem of the generalized mixed nonlinear Schrödinger (GMNLS) equation with finite density type initial data. Based on the spectral analysis of the Lax pair associated with the GMNLS equation, we construct the basic Riemann-Hilbert problem and formally provide the expression of the potential function associated with its solution. The key to the steepest descent method is that the moduli of the different exponential terms, after triangular factorization of the jump matrix, decay in the corresponding regions. On this basis, we establish a mixed -Riemann-Hilbert problem, which can be decomposed into a pure Riemann-Hilbert problem and a pure problem. We solve the pure Riemann-Hilbert problem by scaling and translation to match it to a parabolic cylinder model problem and discuss the existence of solutions to the pure -problem. Finally, the long-time asymptotic behavior of the solution to the GMNLS equation in regions and is obtained.
{"title":"Long-time asymptotics for the generalized mixed nonlinear Schrödinger equation with finite density type initial data","authors":"Wenhao Liu, Yufeng Zhang, Zhenbo Wang","doi":"10.1016/j.physd.2025.135053","DOIUrl":"10.1016/j.physd.2025.135053","url":null,"abstract":"<div><div>In this paper, we apply Riemann-Hilbert approach and <span><math><mover><mi>∂</mi><mo>¯</mo></mover></math></span> steepest descent method to study the Cauchy problem of the generalized mixed nonlinear Schrödinger (GMNLS) equation with finite density type initial data. Based on the spectral analysis of the Lax pair associated with the GMNLS equation, we construct the basic Riemann-Hilbert problem and formally provide the expression of the potential function associated with its solution. The key to the <span><math><mover><mi>∂</mi><mo>¯</mo></mover></math></span> steepest descent method is that the moduli of the different exponential terms, after triangular factorization of the jump matrix, decay in the corresponding regions. On this basis, we establish a mixed <span><math><mover><mi>∂</mi><mo>¯</mo></mover></math></span>-Riemann-Hilbert problem, which can be decomposed into a pure Riemann-Hilbert problem and a pure <span><math><mover><mi>∂</mi><mo>¯</mo></mover></math></span> problem. We solve the pure Riemann-Hilbert problem by scaling and translation to match it to a parabolic cylinder model problem and discuss the existence of solutions to the pure <span><math><mover><mi>∂</mi><mo>¯</mo></mover></math></span>-problem. Finally, the long-time asymptotic behavior of the solution to the GMNLS equation in regions <span><math><mrow><mrow><mo>|</mo></mrow><mfrac><mrow><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mi>ξ</mi><mo>−</mo><mn>2</mn><mi>b</mi></mrow><msup><mi>a</mi><mn>2</mn></msup></mfrac><mrow><mo>|</mo><mo>></mo><mn>1</mn></mrow></mrow></math></span> and <span><math><mrow><mrow><mo>|</mo></mrow><mfrac><mrow><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mi>ξ</mi><mo>−</mo><mn>2</mn><mi>b</mi></mrow><msup><mi>a</mi><mn>2</mn></msup></mfrac><mrow><mo>|</mo><mo><</mo><mn>1</mn></mrow></mrow></math></span> is obtained.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135053"},"PeriodicalIF":2.9,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145652028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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