Pub Date : 2026-03-01Epub 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":"2026-03-01","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 : 2026-03-01Epub Date: 2025-12-17DOI: 10.1016/j.physd.2025.135082
A. Bandera , S. Fernández-García , M. Gómez-Mármol , A. Vidal
We present a novel methodology that combines machine learning techniques with dynamical analysis to classify and interpret the behavior distribution of network models of coupled dynamical systems. Our methodology determines the optimal number of distinct behaviors and classifies them based on time-series features, allowing for an interpretable and automated partition of the parameter space. Applying this approach to a homogeneous two-clusters model of intracellular calcium concentration dynamics, we identify nine different long-term behaviors, including complex and chaotic regimes, mapping experimental data available in the literature. The results highlight the complementarity between data-driven classification and classical dynamical analysis in capturing rich synchronization patterns and detecting subtle transitions in multiple timescale biological systems.
{"title":"Machine learning techniques to identify synchronization patterns in multiple timescale dynamical systems networks","authors":"A. Bandera , S. Fernández-García , M. Gómez-Mármol , A. Vidal","doi":"10.1016/j.physd.2025.135082","DOIUrl":"10.1016/j.physd.2025.135082","url":null,"abstract":"<div><div>We present a novel methodology that combines machine learning techniques with dynamical analysis to classify and interpret the behavior distribution of network models of coupled dynamical systems. Our methodology determines the optimal number of distinct behaviors and classifies them based on time-series features, allowing for an interpretable and automated partition of the parameter space. Applying this approach to a homogeneous two-clusters model of intracellular calcium concentration dynamics, we identify nine different long-term behaviors, including complex and chaotic regimes, mapping experimental data available in the literature. The results highlight the complementarity between data-driven classification and classical dynamical analysis in capturing rich synchronization patterns and detecting subtle transitions in multiple timescale biological systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135082"},"PeriodicalIF":2.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841956","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 : 2026-03-01Epub Date: 2025-12-14DOI: 10.1016/j.physd.2025.135083
M.A. Rehman , M.J. Iqbal , Zeeshan Iqbal , H.A. Shah
The effect of adiabatic trapping in electron-positron-ion (epi) plasmas plays a crucial role in the formation and evolution of drift double-layer (DL) structures, with significant implications for both space and laboratory plasmas. In this study, we investigate the influence of adiabatic trapping, a microscopic phenomenon, on the evolution of drift DLs in epi plasma. Using the Sagdeev potential method, we investigate the conditions necessary to form electrostatic drift DL solutions in epitaxial plasma. Our analysis reveals that key parameters, such as positron concentration, ion drift speed, and the electron-to-positron temperature ratio, significantly influence the formation of drift DLs and their nonlinear characteristics. Notably, only compressive drift DLs are observed, with their amplitude varying based on changes in plasma parameters. Furthermore, the nonlinear dynamical response of the system to external periodic forcing exhibits a rich spectrum of behaviors, including periodic (e.g., period-2 and period-3), quasiperiodic, and chaotic regimes. To the best of our knowledge, this is the first study to conduct a nonlinear dynamical analysis of drift double layers in epi plasmas under external periodic forcing while incorporating adiabatic trapping effects. This work provides new insights into the interplay of microphysical trapping and external drivers in shaping nonlinear plasma structures, thereby advancing the understanding of DL dynamics in space, astrophysical, and laboratory environments.
{"title":"Chaos and order in drift double layers: Nonlinear dynamics in epi plasmas with adiabatic trapping","authors":"M.A. Rehman , M.J. Iqbal , Zeeshan Iqbal , H.A. Shah","doi":"10.1016/j.physd.2025.135083","DOIUrl":"10.1016/j.physd.2025.135083","url":null,"abstract":"<div><div>The effect of adiabatic trapping in electron-positron-ion (<em>epi</em>) plasmas plays a crucial role in the formation and evolution of drift double-layer (<em>DL</em>) structures, with significant implications for both space and laboratory plasmas. In this study, we investigate the influence of adiabatic trapping, a microscopic phenomenon, on the evolution of drift <em>DLs</em> in <em>epi</em> plasma. Using the Sagdeev potential method, we investigate the conditions necessary to form electrostatic drift DL solutions in epitaxial plasma. Our analysis reveals that key parameters, such as positron concentration, ion drift speed, and the electron-to-positron temperature ratio, significantly influence the formation of drift <em>DLs</em> and their nonlinear characteristics. Notably, only compressive drift <em>DLs</em> are observed, with their amplitude varying based on changes in plasma parameters. Furthermore, the nonlinear dynamical response of the system to external periodic forcing exhibits a rich spectrum of behaviors, including periodic (e.g., period-2 and period-3), quasiperiodic, and chaotic regimes. To the best of our knowledge, this is the first study to conduct a nonlinear dynamical analysis of drift double layers in <em>epi</em> plasmas under external periodic forcing while incorporating adiabatic trapping effects. This work provides new insights into the interplay of microphysical trapping and external drivers in shaping nonlinear plasma structures, thereby advancing the understanding of <em>DL</em> dynamics in space, astrophysical, and laboratory environments.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135083"},"PeriodicalIF":2.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766054","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 : 2026-03-01Epub Date: 2025-12-12DOI: 10.1016/j.physd.2025.135074
Uday Chand De , Füsun ÖZEN ZENGİN , Sezgin ALTAY DEMIRBAG , Krishnendu De
In the present paper, we investigate the classification of a spacetime admitting gradient Ricci-Yamabe solitons in special conditions. We acquire that such a spacetime obeying divergence-free Weyl tensor becomes a generalized Robertson-Walker spacetime as well as a static spacetime and the spacetime represents dark matter era. Also, we show that such a spacetime is a Robertson-Walker spacetime and it is of Petrov type “O”. Moreover, it has also been investigated under what conditions this spacetime turns into a stiff matter era. In the last section of this paper, we examine the effect of this spacetime under f(R)-gravity scenario and derive several energy conditions graphically using two different models.
{"title":"Characterizations of a spacetime admitting gradient Ricci-Yamabe solitons and f(R)-gravity","authors":"Uday Chand De , Füsun ÖZEN ZENGİN , Sezgin ALTAY DEMIRBAG , Krishnendu De","doi":"10.1016/j.physd.2025.135074","DOIUrl":"10.1016/j.physd.2025.135074","url":null,"abstract":"<div><div>In the present paper, we investigate the classification of a spacetime admitting gradient Ricci-Yamabe solitons in special conditions. We acquire that such a spacetime obeying divergence-free Weyl tensor becomes a generalized Robertson-Walker spacetime as well as a static spacetime and the spacetime represents dark matter era. Also, we show that such a spacetime is a Robertson-Walker spacetime and it is of Petrov type “O”. Moreover, it has also been investigated under what conditions this spacetime turns into a stiff matter era. In the last section of this paper, we examine the effect of this spacetime under <em>f</em>(<em>R</em>)-gravity scenario and derive several energy conditions graphically using two different models.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135074"},"PeriodicalIF":2.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799701","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 : 2026-03-01Epub Date: 2025-12-09DOI: 10.1016/j.physd.2025.135077
Ulrich Simo Domguia , Vinod V , Bipin Balaram , Paul Woafo
In this work, we consider the Grudzinski-Zebrowski oscillator excited periodically and analyze its dynamical behaviors with reference to the effects of external stimuli on electric node of the heart. Mathematical analysis, numerical and microcontroller simulations are employed. The nonlinear differential equation of the GZ oscillator is solved both analytically and numerically using averaging and the four-order Runge-Kutta methods. The results obtained are shown in terms of asymptotic solution, bifurcation diagrams, corresponding Lyapunov exponents variation and time histories. The bifurcation diagrams reveal the presence of winding number, chaos, bursting, spiking and pulse oscillations. The analytical calculations match well with the numerical results. These behaviors are exhibited experimentally using microcontroller simulations with a good qualitative agreement.
{"title":"Characterization of the dynamics of free and excited Grudzinski-Zebrowski (GZ) oscillator using mathematical methods and microcontroller simulation experiment","authors":"Ulrich Simo Domguia , Vinod V , Bipin Balaram , Paul Woafo","doi":"10.1016/j.physd.2025.135077","DOIUrl":"10.1016/j.physd.2025.135077","url":null,"abstract":"<div><div>In this work, we consider the Grudzinski-Zebrowski oscillator excited periodically and analyze its dynamical behaviors with reference to the effects of external stimuli on electric node of the heart. Mathematical analysis, numerical and microcontroller simulations are employed. The nonlinear differential equation of the GZ oscillator is solved both analytically and numerically using averaging and the four-order Runge-Kutta methods. The results obtained are shown in terms of asymptotic solution, bifurcation diagrams, corresponding Lyapunov exponents variation and time histories. The bifurcation diagrams reveal the presence of winding number, chaos, bursting, spiking and pulse oscillations. The analytical calculations match well with the numerical results. These behaviors are exhibited experimentally using microcontroller simulations with a good qualitative agreement.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135077"},"PeriodicalIF":2.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766053","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 : 2026-03-01Epub Date: 2025-12-12DOI: 10.1016/j.physd.2025.135080
Pedro Gatón-Pérez , Enrique Rodríguez-Fernández , Rodolfo Cuerno
The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully understood. Here we formulate and study a family of conserved stochastic evolution equations for one-dimensional interfaces, whose nonlinearity depends on a parameter n, thus generalizing that of the stochastic Burgers equation, whose behavior is retrieved for . This family of equations includes as particular instances a stochastic porous medium equation and other continuum models relevant to various hard and soft condensed matter systems. We perform a one-loop dynamical renormalization group analysis of the equations, which contemplates strong coupling scaling exponents that depend on the value of n and may or may not imply vertex renormalization. These analytical expectations are contrasted with explicit numerical simulations of the equations with and 3. For odd n, numerical stability issues have required us to generalize the scheme originally proposed for by T. Sasamoto and H. Spohn [J. Stat. Phys. 137, 917 (2009)]. Precisely for and 3, and at variance with the and 2 cases (whose numerical exponents are consistent with non-renormalization of the vertex), numerical strong coupling exponent values are obtained which suggest vertex renormalization, akin to that reported for the celebrated conserved Kardar-Parisi-Zhang (cKPZ) equation. We also study numerically the statistics of height fluctuations, whose probability distribution function turns out (at variance with cKPZ) to have zero skewness for long times and at saturation, irrespective of the value of n. However, the kurtosis is non-Gaussian, further supporting the conclusion on strong coupling asymptotic behavior. The zero skewness seems related with space symmetries of the and 2 equations, and with an emergent symmetry at the strong coupling fixed point for odd values of n.
对于动力学守恒但不一定变分的动力学粗糙界面，其强耦合或非线性标度行为的发生仍有待充分理解。本文建立并研究了一类非线性依赖于参数n的一维界面的守恒随机演化方程，从而推广了n=0时可获取其行为的随机Burgers方程。这一系列方程包括随机多孔介质方程和其他与各种硬、软凝聚态系统相关的连续介质模型。我们对方程进行了一个单环动态重整化群分析，该分析考虑了依赖于n值的强耦合缩放指数，并且可能或可能不意味着顶点重整化。这些分析期望与n= 1,2,3的方程的显式数值模拟进行了对比。对于奇数n，数值稳定性问题要求我们推广最初由T. Sasamoto和H. Spohn在n=0时提出的方案[J]。[j].物理学报，2003,17(5)。精确地说，对于n=1和3，并与n=0和2的情况（其数值指数与顶点的非重整化一致）不同，得到了数值强耦合指数值，表明顶点重整化，类似于著名的保守kardar - paris - zhang （cKPZ）方程的报告。我们还研究了高度波动的数值统计，其概率分布函数（与cKPZ不同）在长时间和饱和时，无论n的值如何，都具有零偏度。然而，峰度是非高斯的，进一步支持了强耦合渐近行为的结论。零偏度似乎与n=0和n= 2方程的空间对称性有关，并且与奇数n值的强耦合不动点的突现对称性有关。
{"title":"Universality classes with strong coupling in conserved surface roughening: explicit vs emergent symmetries","authors":"Pedro Gatón-Pérez , Enrique Rodríguez-Fernández , Rodolfo Cuerno","doi":"10.1016/j.physd.2025.135080","DOIUrl":"10.1016/j.physd.2025.135080","url":null,"abstract":"<div><div>The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully understood. Here we formulate and study a family of conserved stochastic evolution equations for one-dimensional interfaces, whose nonlinearity depends on a parameter <em>n</em>, thus generalizing that of the stochastic Burgers equation, whose behavior is retrieved for <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span>. This family of equations includes as particular instances a stochastic porous medium equation and other continuum models relevant to various hard and soft condensed matter systems. We perform a one-loop dynamical renormalization group analysis of the equations, which contemplates strong coupling scaling exponents that depend on the value of <em>n</em> and may or may not imply vertex renormalization. These analytical expectations are contrasted with explicit numerical simulations of the equations with <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo></mrow></math></span> and 3. For odd <em>n</em>, numerical stability issues have required us to generalize the scheme originally proposed for <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span> by T. Sasamoto and H. Spohn [J. Stat. Phys. <strong>137</strong>, 917 (2009)]. Precisely for <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span> and 3, and at variance with the <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span> and 2 cases (whose numerical exponents are consistent with non-renormalization of the vertex), numerical strong coupling exponent values are obtained which suggest vertex renormalization, akin to that reported for the celebrated conserved Kardar-Parisi-Zhang (cKPZ) equation. We also study numerically the statistics of height fluctuations, whose probability distribution function turns out (at variance with cKPZ) to have zero skewness for long times and at saturation, irrespective of the value of <em>n</em>. However, the kurtosis is non-Gaussian, further supporting the conclusion on strong coupling asymptotic behavior. The zero skewness seems related with space symmetries of the <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span> and 2 equations, and with an emergent symmetry at the strong coupling fixed point for odd values of <em>n</em>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135080"},"PeriodicalIF":2.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766052","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 : 2026-02-01Epub 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":"2026-02-01","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}
Pub Date : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub Date: 2025-12-03DOI: 10.1016/j.physd.2025.135058
Jeong-Min Lee , Hang-Hyun Jo
The visibility graph (VG) algorithm and its variants have been extensively studied in the time series analysis as they transform the time series into the network of nodes and links, enabling to characterize the time series in terms of network measures such as degree distributions. Despite numerous practical applications of VGs in various disciplines, analytical, rigorous understanding of VGs for the correlated time series is still far from complete due to the lack of mathematical tools for modeling the correlation structure in the time series in a tractable form. In this work, we adopt the Farlie-Gumbel-Morgenstern (FGM) copula method to derive the analytical solutions of degree distributions of the horizontal visibility graph (HVG) and its directed version (DHVG) for the correlated time series. Our analytical results show exactly how the correlation between consecutive data points affects the degree distributions of HVGs and DHVGs up to the first order of the correlation parameter in the FGM copula. Thus, our findings shed light on the rigorous understanding of the VG algorithms.
{"title":"Copula-based analytical results of horizontal visibility graphs for correlated time series","authors":"Jeong-Min Lee , Hang-Hyun Jo","doi":"10.1016/j.physd.2025.135058","DOIUrl":"10.1016/j.physd.2025.135058","url":null,"abstract":"<div><div>The visibility graph (VG) algorithm and its variants have been extensively studied in the time series analysis as they transform the time series into the network of nodes and links, enabling to characterize the time series in terms of network measures such as degree distributions. Despite numerous practical applications of VGs in various disciplines, analytical, rigorous understanding of VGs for the correlated time series is still far from complete due to the lack of mathematical tools for modeling the correlation structure in the time series in a tractable form. In this work, we adopt the Farlie-Gumbel-Morgenstern (FGM) copula method to derive the analytical solutions of degree distributions of the horizontal visibility graph (HVG) and its directed version (DHVG) for the correlated time series. Our analytical results show exactly how the correlation between consecutive data points affects the degree distributions of HVGs and DHVGs up to the first order of the correlation parameter in the FGM copula. Thus, our findings shed light on the rigorous understanding of the VG algorithms.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135058"},"PeriodicalIF":2.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748524","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 : 2026-02-01Epub 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.
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