Pub Date : 2025-10-29DOI: 10.1016/j.physd.2025.134994
Yan Wu , Hong-Kun Zhang , Huagui Duan
Understanding the behavior of dynamical systems and their underlying physical laws has long been a central focus of research. However, previous approaches often suffer from either high data and computational demands or an inability to infer the underlying physical laws. In this paper, we propose a novel State–Hamiltonian Neural Network (State–HNN) framework that simultaneously learns a mapping from time to system state and infers the underlying Hamiltonian dynamics. Leveraging Hamiltonian mechanics, the proposed method enforces energy conservation and yields physically consistent predictions. We evaluate the method on several benchmark systems: (1) a mass–spring system; (2) a double pendulum; (3) a simple pendulum; and (4) a three-body system. In particular, we provide a detailed analysis of the three-body experiment. The results demonstrate that State–HNN accurately captures complex dynamics while preserving energy invariance, outperforming the classical Hamiltonian Neural Network (HNN) approach, particularly in high-dimensional settings.
{"title":"State–Hamiltonian Neural Networks for learning dynamical systems","authors":"Yan Wu , Hong-Kun Zhang , Huagui Duan","doi":"10.1016/j.physd.2025.134994","DOIUrl":"10.1016/j.physd.2025.134994","url":null,"abstract":"<div><div>Understanding the behavior of dynamical systems and their underlying physical laws has long been a central focus of research. However, previous approaches often suffer from either high data and computational demands or an inability to infer the underlying physical laws. In this paper, we propose a novel State–Hamiltonian Neural Network (State–HNN) framework that simultaneously learns a mapping from time to system state and infers the underlying Hamiltonian dynamics. Leveraging Hamiltonian mechanics, the proposed method enforces energy conservation and yields physically consistent predictions. We evaluate the method on several benchmark systems: (1) a mass–spring system; (2) a double pendulum; (3) a simple pendulum; and (4) a three-body system. In particular, we provide a detailed analysis of the three-body experiment. The results demonstrate that State–HNN accurately captures complex dynamics while preserving energy invariance, outperforming the classical Hamiltonian Neural Network (HNN) approach, particularly in high-dimensional settings.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134994"},"PeriodicalIF":2.9,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416425","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 : 2025-10-29DOI: 10.1016/j.physd.2025.135011
Rita I. Babicheva , Igor A. Shepelev , Evgeny K. Naumov , Daxing Xiong , Aleksey A. Kudreyko , Sergey V. Dmitriev
The phenomenon of energy localization in nonlinear lattices is of interest to both fundamental science and crystal physics. Localized energy can help overcome potential barriers to defect migration or initiation, which is a topic of significant scientific and practical importance. In real lattices, such as crystal lattices, the presence of inevitable perturbations necessitates a shift in research focus from finding exact discrete breather solutions towards the long-lived quasi-breather (qB) solutions. Higher-dimensional lattices support different qBs with different symmetries, and it is important to know the conditions for their existence. In crystals, long-range interactions, such as metallic or Coulomb interactions, can play an important role. In the present work, the search for qBs in the square -FPUT lattice is continued, taking into account interactions up to the fourth neighbor. The search for qBs is carried out under the assumption that the stiffness of the bonds decreases with their length, as is expected for chemical bonds in crystals. New qBs are identified in comparison to the lattice with short interactions, and it is demonstrated that some of them can move along the lattice, transporting energy.
{"title":"Quasi-breathers in square lattice with long-range interactions","authors":"Rita I. Babicheva , Igor A. Shepelev , Evgeny K. Naumov , Daxing Xiong , Aleksey A. Kudreyko , Sergey V. Dmitriev","doi":"10.1016/j.physd.2025.135011","DOIUrl":"10.1016/j.physd.2025.135011","url":null,"abstract":"<div><div>The phenomenon of energy localization in nonlinear lattices is of interest to both fundamental science and crystal physics. Localized energy can help overcome potential barriers to defect migration or initiation, which is a topic of significant scientific and practical importance. In real lattices, such as crystal lattices, the presence of inevitable perturbations necessitates a shift in research focus from finding exact discrete breather solutions towards the long-lived quasi-breather (qB) solutions. Higher-dimensional lattices support different qBs with different symmetries, and it is important to know the conditions for their existence. In crystals, long-range interactions, such as metallic or Coulomb interactions, can play an important role. In the present work, the search for qBs in the square <span><math><mi>β</mi></math></span>-FPUT lattice is continued, taking into account interactions up to the fourth neighbor. The search for qBs is carried out under the assumption that the stiffness of the bonds decreases with their length, as is expected for chemical bonds in crystals. New qBs are identified in comparison to the lattice with short interactions, and it is demonstrated that some of them can move along the lattice, transporting energy.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135011"},"PeriodicalIF":2.9,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145425689","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 : 2025-10-28DOI: 10.1016/j.physd.2025.135002
Wenjing Xing , Nan Liu , Jinyi Sun
In this study, we present a systematical inverse scattering transform for the matrix modified Korteweg–de Vries (mKdV) equation with the associated analytic scattering coefficients consisting of pairs of higher-order zeros. The analyticity properties and symmetries of the Jost eigenfunctions and scattering coefficients are discussed in the direct problem. In particular, discrete spectrum associated with these pairs of multiple zeros is analyzed explicitly. Next, we formulate a 4 × 4 matrix Riemann–Hilbert (RH) problem that incorporates the residue conditions at these higher-order poles. By solving this RH problem, we obtain the reconstruction formula for the solution of the matrix mKdV equation. Under the reflectionless condition, the associated RH problem can be reduced to a system of linear algebraic equations. We demonstrate that the solution to this system exists and is unique, allowing us to explicitly derive the higher-order soliton solutions.
{"title":"On the inverse scattering transform for the matrix mKdV equation with multiple higher-order poles","authors":"Wenjing Xing , Nan Liu , Jinyi Sun","doi":"10.1016/j.physd.2025.135002","DOIUrl":"10.1016/j.physd.2025.135002","url":null,"abstract":"<div><div>In this study, we present a systematical inverse scattering transform for the matrix modified Korteweg–de Vries (mKdV) equation with the associated analytic scattering coefficients consisting of <span><math><mi>N</mi></math></span> pairs of higher-order zeros. The analyticity properties and symmetries of the Jost eigenfunctions and scattering coefficients are discussed in the direct problem. In particular, discrete spectrum associated with these <span><math><mi>N</mi></math></span> pairs of multiple zeros is analyzed explicitly. Next, we formulate a 4 × 4 matrix Riemann–Hilbert (RH) problem that incorporates the residue conditions at these higher-order poles. By solving this RH problem, we obtain the reconstruction formula for the solution of the matrix mKdV equation. Under the reflectionless condition, the associated RH problem can be reduced to a system of linear algebraic equations. We demonstrate that the solution to this system exists and is unique, allowing us to explicitly derive the higher-order soliton solutions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 135002"},"PeriodicalIF":2.9,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416515","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 : 2025-10-27DOI: 10.1016/j.physd.2025.135008
Junchao Chen , Jin Song , Ming Zhong , Zhenya Yan
We, based on the extended physics-informed neural networks (PINNs), propose a stepwise multi-stage training strategy with the U-shaped enveloping domain decomposition, in which the collection points are resampled and the pseudo characteristic points are introduced at the next stage of training, and transfer learning are employed between two successive stages. The modified PINNs approach is used to investigate data-driven rogue-wave dynamics and parameter identifications for the Newell-type long-short wave system. For the forward problems, we effectively learn three types of first- and second-order rogue wave solutions including bright, intermediate and dark states in the short-wave component, which belong to a class of localized solutions with the steep gradients. For the inverse problems, we identify the unknown coefficient parameters with and without noises by using the classical PINNs algorithm. In particular, we introduce the characteristic points as internal information points during the training process to improve the convergence rate and prediction accuracy.
{"title":"Modified physics-informed neural networks: Data-driven rogue-wave dynamics and parameter identifications for the Newell-type long-short wave system","authors":"Junchao Chen , Jin Song , Ming Zhong , Zhenya Yan","doi":"10.1016/j.physd.2025.135008","DOIUrl":"10.1016/j.physd.2025.135008","url":null,"abstract":"<div><div>We, based on the extended physics-informed neural networks (PINNs), propose a stepwise multi-stage training strategy with the U-shaped enveloping domain decomposition, in which the collection points are resampled and the pseudo characteristic points are introduced at the next stage of training, and transfer learning are employed between two successive stages. The modified PINNs approach is used to investigate data-driven rogue-wave dynamics and parameter identifications for the Newell-type long-short wave system. For the forward problems, we effectively learn three types of first- and second-order rogue wave solutions including bright, intermediate and dark states in the short-wave component, which belong to a class of localized solutions with the steep gradients. For the inverse problems, we identify the unknown coefficient parameters with and without noises by using the classical PINNs algorithm. In particular, we introduce the characteristic points as internal information points during the training process to improve the convergence rate and prediction accuracy.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135008"},"PeriodicalIF":2.9,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475126","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 : 2025-10-27DOI: 10.1016/j.physd.2025.134998
Shijing Gao , Lili Huang , Yunfei Yue
Consideration herein is a quasilinear generalized nonlocal shallow-water equation for moderate-amplitude equatorial waves with the Coriolis and equatorial undercurrent effects, which can be derived from the incompressible and rotational two-dimensional shallow water in equatorial region according to the formal asymptotic procedures. This resulting equation is related to the b-family equation and the compressible hyperelastic rod model in the material science. Subsequently, the blow-up criterion for the established equation in a suitable Sobolev space is presented without the help of conservation law. Moreover, the influences and interactions of the nonlocal higher nonlinearities, vorticity and weak Coriolis force on wave-breaking phenomena are investigated, as well as the persistence properties of the solutions in weighted spaces. Finally, we provide a sufficient condition for global strong solutions to the generalized nonlocal shallow-water equation in some special case.
{"title":"On a generalized nonlocal shallow-water equation","authors":"Shijing Gao , Lili Huang , Yunfei Yue","doi":"10.1016/j.physd.2025.134998","DOIUrl":"10.1016/j.physd.2025.134998","url":null,"abstract":"<div><div>Consideration herein is a quasilinear generalized nonlocal shallow-water equation for moderate-amplitude equatorial waves with the Coriolis and equatorial undercurrent effects, which can be derived from the incompressible and rotational two-dimensional shallow water in equatorial region according to the formal asymptotic procedures. This resulting equation is related to the b-family equation and the compressible hyperelastic rod model in the material science. Subsequently, the blow-up criterion for the established equation in a suitable Sobolev space is presented without the help of conservation law. Moreover, the influences and interactions of the nonlocal higher nonlinearities, vorticity and weak Coriolis force on wave-breaking phenomena are investigated, as well as the persistence properties of the solutions in weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> spaces. Finally, we provide a sufficient condition for global strong solutions to the generalized nonlocal shallow-water equation in some special case.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134998"},"PeriodicalIF":2.9,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416516","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}
In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation and the solution of these equations. We begin by examining the Cole–Hopf transformation, a classical result that converts the nonlinear, viscous Burgers’ equation into the linear heat equation. We demonstrate that this transformation can be effectively learned using Gaussian process regression, either from single or from multiple initial conditions of the Burgers equation. We then extend our methodology to discover mappings between initial conditions of a nonlinear partial differential equation (PDE) and a linear PDE, where the exact form of the linear PDE remains unknown and is inferred through Computational Graph Completion (CGC), a generalization of Gaussian Process Regression from approximating single input/output functions to approximating multiple input/output functions that interact within a computational graph. Further, we employ CGC to identify a local transformation from the nonlinear ordinary differential equation (ODE) of the Brusselator to its Poincaré normal form, capturing the dynamics around a Hopf bifurcation. Moreover, we interpret our learning procedure through Algorithmic Information Theory (AIT) and the Minimal Description Length (MDL) principle, framing these transformations as efficient, succinct encodings that compress nonlinear dynamics into simpler, linearized representations. This MDL perspective not only provides a theoretical justification for kernel-based regression methods but also illuminates the relationship between kernel learning and principles of model simplicity and data compression showing that learning in a reproducing kernel Hilbert space (RKHS) simultaneously minimizes a proxy for Kolmogorov complexity and maximizes algorithmic mutual information between the data and transformation. We conclude by addressing the broader question of whether systematic transformations between nonlinear and linear PDEs can generally exist, suggesting avenues for future research.
{"title":"Gaussian Processes simplify differential equations","authors":"Jonghyeon Lee , Boumediene Hamzi , Yannis Kevrekidis , Houman Owhadi","doi":"10.1016/j.physd.2025.134988","DOIUrl":"10.1016/j.physd.2025.134988","url":null,"abstract":"<div><div>In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation and the solution of these equations. We begin by examining the Cole–Hopf transformation, a classical result that converts the nonlinear, viscous Burgers’ equation into the linear heat equation. We demonstrate that this transformation can be effectively learned using Gaussian process regression, either from single or from multiple initial conditions of the Burgers equation. We then extend our methodology to discover mappings between initial conditions of a nonlinear partial differential equation (PDE) and a linear PDE, where the exact form of the linear PDE remains unknown and is inferred through Computational Graph Completion (CGC), a generalization of Gaussian Process Regression from approximating single input/output functions to approximating multiple input/output functions that interact within a computational graph. Further, we employ CGC to identify a local transformation from the nonlinear ordinary differential equation (ODE) of the Brusselator to its Poincaré normal form, capturing the dynamics around a Hopf bifurcation. Moreover, we interpret our learning procedure through Algorithmic Information Theory (AIT) and the Minimal Description Length (MDL) principle, framing these transformations as efficient, succinct encodings that compress nonlinear dynamics into simpler, linearized representations. This MDL perspective not only provides a theoretical justification for kernel-based regression methods but also illuminates the relationship between kernel learning and principles of model simplicity and data compression showing that learning in a reproducing kernel Hilbert space (RKHS) simultaneously minimizes a proxy for Kolmogorov complexity and maximizes algorithmic mutual information between the data and transformation. We conclude by addressing the broader question of whether systematic transformations between nonlinear and linear PDEs can generally exist, suggesting avenues for future research.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134988"},"PeriodicalIF":2.9,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416427","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 : 2025-10-24DOI: 10.1016/j.physd.2025.135007
Sanaa L. Khalaf, Akil J. Harfash
We study solutal convection in a Brinkman porous layer with generalised Robin boundary conditions for solute concentration and two-sided Navier slip for velocity. The linear onset threshold () and the global energy threshold () are determined using a new Chebyshev collocation algorithm coupled to a pseudoinverse–eigenvalue formulation and a golden–section search. Accuracy is assessed through residual evaluation, as no analytical solutions are available for this problem. The results reveal that the Brinkman coefficient exerts a nearly linear stabilising influence on both and , while the slip coefficients and act asymmetrically to destabilise the system. In addition, the interaction between the reaction parameter and the concentration ratio produces non-monotonic shifts in the stability thresholds. These findings clarify how reaction, solute exchange, and interfacial slip reshape both linear and nonlinear stability boundaries in Brinkman porous media, and they establish a high-accuracy computational framework for analysing stability regimes relevant to reactive transport.
{"title":"Hydrodynamic stability of convection in porous medium with chemical reaction effect and generalised boundary conditions","authors":"Sanaa L. Khalaf, Akil J. Harfash","doi":"10.1016/j.physd.2025.135007","DOIUrl":"10.1016/j.physd.2025.135007","url":null,"abstract":"<div><div>We study solutal convection in a Brinkman porous layer with generalised Robin boundary conditions for solute concentration and two-sided Navier slip for velocity. The linear onset threshold (<span><math><mrow><mi>R</mi><msub><mrow><mi>a</mi></mrow><mrow><mi>L</mi></mrow></msub></mrow></math></span>) and the global energy threshold (<span><math><mrow><mi>R</mi><msub><mrow><mi>a</mi></mrow><mrow><mi>E</mi></mrow></msub></mrow></math></span>) are determined using a new Chebyshev collocation algorithm coupled to a pseudoinverse–eigenvalue formulation and a golden–section search. Accuracy is assessed through residual evaluation, as no analytical solutions are available for this problem. The results reveal that the Brinkman coefficient <span><math><mi>λ</mi></math></span> exerts a nearly linear stabilising influence on both <span><math><mrow><mi>R</mi><msub><mrow><mi>a</mi></mrow><mrow><mi>L</mi></mrow></msub></mrow></math></span> and <span><math><mrow><mi>R</mi><msub><mrow><mi>a</mi></mrow><mrow><mi>E</mi></mrow></msub></mrow></math></span>, while the slip coefficients <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>L</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>U</mi></mrow></msub></math></span> act asymmetrically to destabilise the system. In addition, the interaction between the reaction parameter <span><math><mi>ζ</mi></math></span> and the concentration ratio <span><math><mi>η</mi></math></span> produces non-monotonic shifts in the stability thresholds. These findings clarify how reaction, solute exchange, and interfacial slip reshape both linear and nonlinear stability boundaries in Brinkman porous media, and they establish a high-accuracy computational framework for analysing stability regimes relevant to reactive transport.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 135007"},"PeriodicalIF":2.9,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416514","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 : 2025-10-24DOI: 10.1016/j.physd.2025.134983
Chengjie Zhan , Zhenhua Chai , Dongke Sun , Shaoning Geng , Ping Jiang , Baochang Shi
In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas–liquid–dendrite system is proposed through considering the interactions of gas bubbles, liquid melt and solid dendrites, and it can reduce to the energy for gas–liquid flows in the region far from the solid phase, while degenerate to the energy for thermosolutal dendritic growth when the gas bubble disappears. The governing equations are usually obtained by minimizing the total free energy, but here some modifications are made to improve the capacity of the conservative phase-field equation for gas bubbles and convection–diffusion equation for solute transfer. Additionally, through the asymptotic analysis of the thin-interface limit, the part of present general phase-field model for alloy solidification can match the corresponding free boundary problem, and it is identical to the commonly used models under a specific choice of model parameters. Furthermore, to describe the fluid flow, the incompressible Navier–Stokes equations are adopted in the entire domain including gas, liquid, and solid regions, where the fluid–structure interaction is considered by a simple diffuse-interface method. To test the present phase-field model, the lattice Boltzmann method is used to study several problems of gas–liquid flows, dendritic growth as well as the solidification in presence of gas bubbles, and a good performance of the present model for such complex problems is observed.
{"title":"Phase-field modeling of dendritic growth with gas bubbles in the solidification of binary alloys","authors":"Chengjie Zhan , Zhenhua Chai , Dongke Sun , Shaoning Geng , Ping Jiang , Baochang Shi","doi":"10.1016/j.physd.2025.134983","DOIUrl":"10.1016/j.physd.2025.134983","url":null,"abstract":"<div><div>In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas–liquid–dendrite system is proposed through considering the interactions of gas bubbles, liquid melt and solid dendrites, and it can reduce to the energy for gas–liquid flows in the region far from the solid phase, while degenerate to the energy for thermosolutal dendritic growth when the gas bubble disappears. The governing equations are usually obtained by minimizing the total free energy, but here some modifications are made to improve the capacity of the conservative phase-field equation for gas bubbles and convection–diffusion equation for solute transfer. Additionally, through the asymptotic analysis of the thin-interface limit, the part of present general phase-field model for alloy solidification can match the corresponding free boundary problem, and it is identical to the commonly used models under a specific choice of model parameters. Furthermore, to describe the fluid flow, the incompressible Navier–Stokes equations are adopted in the entire domain including gas, liquid, and solid regions, where the fluid–structure interaction is considered by a simple diffuse-interface method. To test the present phase-field model, the lattice Boltzmann method is used to study several problems of gas–liquid flows, dendritic growth as well as the solidification in presence of gas bubbles, and a good performance of the present model for such complex problems is observed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134983"},"PeriodicalIF":2.9,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416417","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 : 2025-10-24DOI: 10.1016/j.physd.2025.134984
Paolo Antonelli , David N. Reynolds
We study the well known Schrödinger–Lohe model for quantum synchronization with non-identical natural frequencies. The main results are related to the characterization and convergence to phase-locked states for this quantum system. The results of this article are four-fold. Via a characterization of the fixed points of the system of correlations, we uncover a direct correspondence to the fixed points of the classical Kuramoto model. Depending on the coupling strength, , relative to natural frequencies, , a Lyapunov function is revealed which drives the system to the phase-locked state exponentially fast. Explicit bounds on the asymptotic configurations are granted via a parametric analysis. Finally, linear stability (instability) of the fixed points is provided via an eigenvalue perturbation argument.
{"title":"Lyapunov stability and exponential phase-locking of Schrödinger–Lohe quantum oscillators","authors":"Paolo Antonelli , David N. Reynolds","doi":"10.1016/j.physd.2025.134984","DOIUrl":"10.1016/j.physd.2025.134984","url":null,"abstract":"<div><div>We study the well known Schrödinger–Lohe model for quantum synchronization with non-identical natural frequencies. The main results are related to the characterization and convergence to phase-locked states for this quantum system. The results of this article are four-fold. Via a characterization of the fixed points of the system of correlations, we uncover a direct correspondence to the fixed points of the classical Kuramoto model. Depending on the coupling strength, <span><math><mi>κ</mi></math></span>, relative to natural frequencies, <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>, a Lyapunov function is revealed which drives the system to the phase-locked state exponentially fast. Explicit bounds on the asymptotic configurations are granted via a parametric analysis. Finally, linear stability (instability) of the fixed points is provided via an eigenvalue perturbation argument.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134984"},"PeriodicalIF":2.9,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416420","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 : 2025-10-24DOI: 10.1016/j.physd.2025.134961
Uditnarayan Kouskiya , Robert L. Pego , Amit Acharya
We look for traveling waves of the semi-discrete conservation law , using variational principles related to concepts of “hidden convexity” appearing in recent studies of various PDE (partial differential equations). We analyze and numerically compute with two variational formulations related to dual convex optimization problems constrained by either the differential-difference equation (DDE) or nonlinear integral equation (NIE) that wave profiles should satisfy. We prove existence theorems conditional on the existence of extrema that satisfy a strict convexity criterion, and numerically exhibit a variety of localized, periodic and non-periodic wave phenomena.
{"title":"Traveling wave profiles for a semi-discrete Burgers equation","authors":"Uditnarayan Kouskiya , Robert L. Pego , Amit Acharya","doi":"10.1016/j.physd.2025.134961","DOIUrl":"10.1016/j.physd.2025.134961","url":null,"abstract":"<div><div>We look for traveling waves of the semi-discrete conservation law <span><math><mrow><mn>4</mn><msub><mrow><mover><mrow><mi>u</mi></mrow><mrow><mo>̇</mo></mrow></mover></mrow><mrow><mi>j</mi></mrow></msub><mo>+</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>−</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mi>j</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>0</mn></mrow></math></span>, using variational principles related to concepts of “hidden convexity” appearing in recent studies of various PDE (partial differential equations). We analyze and numerically compute with two variational formulations related to dual convex optimization problems constrained by either the differential-difference equation (DDE) or nonlinear integral equation (NIE) that wave profiles should satisfy. We prove existence theorems conditional on the existence of extrema that satisfy a strict convexity criterion, and numerically exhibit a variety of localized, periodic and non-periodic wave phenomena.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134961"},"PeriodicalIF":2.9,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416422","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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