Physica D: Nonlinear Phenomena最新文献

英文中文

Multi-pole solitons and breathers with spatially periodic modulation induced by the helicoidal spin-orbit coupling 螺旋自旋轨道耦合诱导的空间周期调制多极孤子和呼吸子

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-02 DOI: 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.

本文报道了具有螺旋形自旋-轨道耦合（SOC）的空间非均匀二元玻色-爱因斯坦凝聚体（BECs）中多种多极孤子和呼吸态的解析解，包括零背景下的多极条纹孤子、非零平面波背景下的多极加热条纹孤子以及周期背景下的多极加热条纹孤子和呼吸态的解析解。结果表明，螺旋形SOC产生的调制效应不仅可以诱导MP孤子中的条纹模式，还可以为MP跳动的条纹孤子和呼吸子产生空间周期背景。渐近分析揭示了这些MP激发的曲线轨迹与对数增加的孤子/呼吸子分离，从根本上将它们与束缚态孤子/呼吸子的周期轨迹或传统多孤子/呼吸子集的直线轨迹区分开来。由于单个组分具有复杂的周期结构，总密度分布是非周期的，这是由于它们的构型相对于两个组分是相外的。我们进一步研究了不同SOC和光谱参数下MP孤子和呼吸子的简并结构。数值模拟验证了分析结果，并证明了这些MP激励的稳定性。这些发现可能有助于在SOC BEC中深入理解传统的多孤子系统和结合态复合物之外的孤子/呼吸子相互作用。

{"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}

引用次数: 0

Koopman representations with irregular time intervals 不规则时间间隔的Koopman表示

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 DOI: 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.

由于Koopman算子理论允许以数据驱动的方式构建动力系统的模态，因此该理论已被广泛应用于动力学控制的实际系统的数据同化问题。在许多现代问题中，这些模式通常必须从具有不规则采样间隔的数据中学习，而不是通常使用的规则采样数据。在这里，我们提出了一个框架来恢复不规则采样数据的库普曼特征函数-特征值对。我们证明了可以通过自然优化问题恢复库普曼特征对。我们对优化中预期的挑战提供技术评论，并建议解决这些挑战的程序。不同不规则采样场景下的仿真研究验证了该方法在学习库普曼特征函数方面的鲁棒性。与对插值重采样数据进行扩展动态模态分解相比，该方法具有更高的特征函数恢复精度。

引用次数: 0

The evasion of tipping: Pattern formation near a Turing-fold bifurcation 引爆的回避：图灵褶皱分岔附近的模式形成

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-29 DOI: 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

n

-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,

β

, is positive. We derive explicit expressions for

β

, 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.

模式研究表明，许多气候子系统，特别是生态系统，可能容易受到临界点的影响：一个系统在逐渐变化的外部因素的驱动下，从理想状态突然过渡（或崩溃）到不理想状态的灾难性过程。在生态系统中，空间模式的出现传统上被解释为可能的预警信号。然而，最近，模式形成被提出了一个根本不同的角色：作为一种机制，通过这种机制，一个（生态）系统可以通过形成稳定的模式来避免引爆，这种模式在引爆点之后持续存在。数学上，引爆通常与鞍节点分岔有关，而模式形成通常由图灵分岔驱动。因此，我们研究了协维2图灵分岔，并探讨了由图灵分岔引发的模式何时能使系统避免引爆？我们开发了一类相场模型的方法，并随后将其应用于n组分反应扩散系统-一类常用于生态系统建模的偏微分方程。我们证明了调制方程的双组分系统控制图灵折叠分岔附近的模式形成，并且当关键参数β为正值时可以避免引爆。我们推导出β的显式表达式，允许人们确定给定系统是否可以避免引爆。此外，我们在数值上表明，该系统表现出丰富的行为，从稳定，平稳，空间准周期模式到不规则，时空，混沌样动态。

{"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}

引用次数: 0

Inverse scattering transform for the coupled Yajima-Oikawa systems 耦合Yajima-Oikawa系统的逆散射变换

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-28 DOI: 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.

利用逆散射变换，导出了边界消失条件下Yajima-Oikawa耦合系统的精确n孤子解。从新提出的Lax对出发，构造了相应的Jost函数，并分析了它们的对称性和解析性。特征函数的积分方程引出了Gel 'fand-Levitan-Marchenko方程的表达式；求解这些关系建立了核函数和势的直接对应关系，得到了一般的n孤子表达式。最后，通过适当的参数选择，用图形说明了n孤子解的结构特征。

引用次数: 0

Small Alfvén number limit for the global-in-time solutions of incompressible MHD equations with general initial data 具有一般初始数据的不可压缩MHD方程全局实时解的小alfvsamn数极限

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-26 DOI: 10.1016/j.physd.2025.135029

Yuan Cai , Xiufang Cui , Fei Jiang , Hao Liu

The small Alfvén number (denoted by

ɛ

) 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

T^{3}

(i.e. a spatially periodic domain) tend to a solution of 2D ideal MHD equations in the distribution sense as

ɛ \to 0

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

R^{n}

with

n = 2

, 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

ɛ \to 0

for any given time–space variable

(x, t)

with

t > 0

. 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}

引用次数: 0

Peregrine soliton and Akhmediev Breather in superthermal multi-ion plasmas and their role in ion-induced nanostructuring 超热多离子等离子体中的Peregrine孤子和Akhmediev呼吸子及其在离子诱导纳米结构中的作用

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-26 DOI: 10.1016/j.physd.2025.135027

N.A. El-Bedwehy , R. Sabry , W.M. Moslem , I.S. Elkamash

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

^{2 +}

, Ti

^{4 +}

, and O

^{2 -}

ions with a

κ

-distribution of electrons. We use weakly nonlinear analysis to develop analytical formulas for the dispersion (

P

) and nonlinear (

Q

) coefficients, methodically investigating their effect on the superthermality index

κ

and ion concentration ratio

β = n_{T 0} / n_{s 0}

We found that reducing

κ

(stronger suprathermal effects) increases anomalous dispersion (

P < 0

) and self-focusing nonlinearity (

Q < 0

), whereas increasing

β

increases modulational instability (

P Q > 0

) via increasing ion inertia and charge density. Localized wave structures are predicted universally by

P Q

. 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.

利用非线性Schrödinger方程（NLSE）研究了多离子超热等离子体中静电波包络的动力学。等离子体中含有Sr2+、Ti4+和O2−离子，电子呈κ-分布。我们利用弱非线性分析建立了色散(P)和非线性(Q)系数的解析公式，系统地研究了它们对超热指数κ和离子浓度比β=nT0/ns0的影响。我们发现，降低κ（更强的超热效应）会增加异常色散（P<0）和自聚焦非线性（Q<0），而增加β会通过增加离子惯性和电荷密度增加调制不稳定性（PQ>0）。用PQ预测局域波结构具有普适性。在NLSE数值解中，Peregrine孤子（瞬态异常波）和Akhmediev呼吸子（周期调制）表现出明显的时空局域性。等离子体密度的变化会导致超出材料内聚力限制的机械应变，在离子照射下导致纳米级表面变形。我们的研究结果为等离子体辅助纳米制造和空间等离子体设置中的纳米结构形态控制提供了一个基于等离子体参数的范例。

{"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}

引用次数: 0

Long-time asymptotics for the generalized mixed nonlinear Schrödinger equation with finite density type initial data 具有有限密度型初始数据的广义混合非线性Schrödinger方程的长时间渐近性

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-25 DOI: 10.1016/j.physd.2025.135053

Wenhao Liu, Yufeng Zhang, Zhenbo Wang

In this paper, we apply Riemann-Hilbert approach and

\bar{\partial}

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

\bar{\partial}

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

\bar{\partial}

-Riemann-Hilbert problem, which can be decomposed into a pure Riemann-Hilbert problem and a pure

\bar{\partial}

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

\bar{\partial}

-problem. Finally, the long-time asymptotic behavior of the solution to the GMNLS equation in regions

| \frac{2 a^{2} + a ξ - 2 b}{a^{2}} | > 1

and

| \frac{2 a^{2} + a ξ - 2 b}{a^{2}} | < 1

is obtained.

在本文中，我们应用Riemann-Hilbert方法和∂¯最陡下降方法来研究具有有限密度型初始数据的广义混合非线性Schrödinger （GMNLS）方程的Cauchy问题。基于对与GMNLS方程相关的Lax对的谱分析，构造了基本的Riemann-Hilbert问题，并形式化地给出了与其解相关的势函数表达式。∂¯最陡下降法的关键在于，在对跳跃矩阵进行三角分解后，不同指数项的模在相应的区域内衰减。在此基础上，我们建立了一个混合∂¯-Riemann-Hilbert问题，它可以分解为一个纯Riemann-Hilbert问题和一个纯∂¯问题。我们通过缩放和平移来解决纯Riemann-Hilbert问题，以将其与抛物柱面模型问题匹配，并讨论纯∂¯问题解的存在性。最后，得到了GMNLS方程解在|a2 +aξ−2ba2|>；1和|a2 +aξ−2ba2|<；1区域的长时间渐近性质。

{"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}

引用次数: 0

Applying canonical transformations to the nonlinear Schrödinger equation for modeling fiber optic communications 应用正则变换对非线性Schrödinger方程进行光纤通信建模

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-25 DOI: 10.1016/j.physd.2025.135049

Sergey Dremov , Dmitry Kachulin , Igor Chekhovskoy , Oleg Sidelnikov , Alexey Redyuk , Alexander Dyachenko

This paper presents a numerical implementation of a novel algorithm for modeling optical signal propagation under the nonlinear Schrödinger equation. Rooted in the Hamiltonian formalism and canonical transformations, the method is mathematically rigorous and devoid of empirical techniques. We investigate the algorithm’s properties and range of applicability both analytically and numerically, highlighting its advantages over existing methods. An extension is also developed to include dissipative effects. The proposed approach is applied to various wave fields, and its performance is compared with standard dispersion and nonlinear phase compensation techniques. These initial results demonstrate the potential of the algorithm for fiber-optic communication applications.

本文给出了一种在非线性Schrödinger方程下模拟光信号传播的新算法的数值实现。该方法植根于哈密顿的形式主义和规范变换，在数学上是严格的，缺乏经验技术。我们从分析和数值两方面研究了该算法的性质和适用范围，突出了它相对于现有方法的优势。还开发了一个扩展，以包括耗散效应。将该方法应用于各种波场，并与标准色散和非线性相位补偿技术进行了性能比较。这些初步结果证明了该算法在光纤通信应用中的潜力。

引用次数: 0

Adiabatic heating strategies in many-body classical systems and plasmas 经典多体系统和等离子体的绝热加热策略

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-22 DOI: 10.1016/j.physd.2025.135041

Roberto Onofrio , Bala Sundaram

We discuss adiabatic strategies for heating a gas of particles harmonically trapped in the presence of another gas of particles which are also harmonically trapped, while also experiencing nonlinear interatomic interactions. These include recently proposed strategies, namely shortcuts to adiabaticity, in which the cooling or heating occurs quickly, at variance with the usual occurrence over times much longer than intrinsic timescales. Using quantitative indicators, we track the extent of adherence to Maxwell-Boltzmann energy distributions of both gases during the compression transient. The model, although aimed at addressing ionized gases, also allows for local and extended interactions, interpolating between the description of neutral atomic gases and ordered condensed matter systems, with plasmas – exhibiting genuine nonlinear behavior – in the intermediate regime.

我们讨论了一种绝热策略，在另一种也被谐波捕获的粒子气体存在的情况下加热谐波捕获的粒子气体，同时也经历了非线性原子相互作用。其中包括最近提出的策略，即绝热的捷径，其中冷却或加热发生得很快，与通常发生的时间比内在时间尺度长得多。利用定量指标，我们跟踪了压缩瞬态过程中两种气体对麦克斯韦-玻尔兹曼能量分布的遵守程度。该模型虽然旨在处理电离气体，但也允许局部和扩展的相互作用，在中性原子气体和有序凝聚态系统的描述之间插入，等离子体-表现出真正的非线性行为-在中间状态。

引用次数: 0

Special solutions to a geometric curvature flow of evaporation–condensation 蒸发-冷凝几何曲率流的特殊解

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-21 DOI: 10.1016/j.physd.2025.135039

Axel Kröner , Heiko Kröner

In this paper we study the evolution of special hypersurfaces in Euclidean space evolving according to a geometric curvature flow which is motivated from the phenomenon of evaporation–condensation and which was introduced in Mullins (1957). The first example is a closed, embedded and convex curve which does not converge to a point under the (smooth) flow. This shows that the flow behaves differently from curve shortening flow. Further we show existence of two examples of hypersurfaces which translate under this evolution. Their shape is motivated from translators as they appear in the theory of mean curvature flow: A complete, unbounded graph over a finite time interval and in the higher dimensional case a rotationally symmetric entire graph over

R^{n}

本文研究了欧几里得空间中特殊超曲面的演化，该曲面是根据Mullins（1957）提出的由蒸发-凝结现象引起的几何曲率流演化而来的。第一个例子是一个封闭的、嵌入的和凸的曲线，它不收敛于（平滑）流下的一点。这表明该流动的特性与缩短曲线流动不同。进一步，我们证明了在这种演化下平移的两个超曲面的存在性。它们的形状源于平均曲率流理论中的翻译：在有限时间间隔内的完整无界图，在高维情况下是Rn上的旋转对称整个图。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Physica D: Nonlinear Phenomena

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀