Pub Date : 2025-11-08DOI: 10.1016/j.physd.2025.135016
Ziqi Ren , Xingwu Chen
As a complement to DC–DC buck converters investigated in previous publications, in this paper we analyze the dynamics of a 3-dimensional Filippov system arising from a DC–DC boost converter, including the singular point bifurcation and the existence of crossing limit cycles. This system has two intersected tangency lines on the switching boundary, which leads to more complicated dynamical behaviors than the buck converter because the latter has two parallel tangency lines. We obtain stability conditions for the intersection point of these two tangency lines in sliding regions and bifurcation conditions for it dividing into several singular points such as standard equilibria, boundary equilibria, cusps, and prove the existence of crossing limit cycles by pseudo-Hopf bifurcations. Finally, our main results are applied to this DC–DC boost converter to explain the reason of boost failure, to find critical parameter values leading to boost failure, to provide strategies for keeping the boost function even if some electrical apparatus elements are changed.
{"title":"Bifurcations and crossing limit cycles of a Filippov system arising from a DC–DC boost converter","authors":"Ziqi Ren , Xingwu Chen","doi":"10.1016/j.physd.2025.135016","DOIUrl":"10.1016/j.physd.2025.135016","url":null,"abstract":"<div><div>As a complement to DC–DC buck converters investigated in previous publications, in this paper we analyze the dynamics of a 3-dimensional Filippov system arising from a DC–DC boost converter, including the singular point bifurcation and the existence of crossing limit cycles. This system has two intersected tangency lines on the switching boundary, which leads to more complicated dynamical behaviors than the buck converter because the latter has two parallel tangency lines. We obtain stability conditions for the intersection point of these two tangency lines in sliding regions and bifurcation conditions for it dividing into several singular points such as standard equilibria, boundary equilibria, cusps, and prove the existence of crossing limit cycles by pseudo-Hopf bifurcations. Finally, our main results are applied to this DC–DC boost converter to explain the reason of boost failure, to find critical parameter values leading to boost failure, to provide strategies for keeping the boost function even if some electrical apparatus elements are changed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135016"},"PeriodicalIF":2.9,"publicationDate":"2025-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-05DOI: 10.1016/j.physd.2025.135018
Zhaoquan Xu , Dongmei Xiao , Chufen Wu
We investigate the traveling wave dynamics in a population model with mobile and stationary states under a changing environment, which is modeled by a partially degenerate reaction–diffusion equation with a moving variable , . We focus on whether the species could keep up with the changing environment, that is, whether the equation model has a forced traveling wave with speed , and how the switching rates between mobile and stationary states affect the propagation dynamics. It is shown that there exists a threshold value , such that the equation model admits a forced traveling wave with speed if and only if the environment shifting speed . Thereby, the species cannot follow the changing environment with speed if . Compared to the well-known results on the classic Fisher’s equation which assumes the population has only mobile state, our result highlights a significant observation: the presence of stationary state in population will reduce the invasion threshold value . Moreover, it is proved that such a forced traveling wave is unique and globally stable if . This implies that the species can successfully invade new environment as a forced wave if the environment shifting speed satisfies . Some numerical simulations are also provided to illustrate the theoretical results and explain the invasion phenomena of species under environmental changes.
{"title":"Forced traveling waves in a population model with mobile and stationary states under a changing environment","authors":"Zhaoquan Xu , Dongmei Xiao , Chufen Wu","doi":"10.1016/j.physd.2025.135018","DOIUrl":"10.1016/j.physd.2025.135018","url":null,"abstract":"<div><div>We investigate the traveling wave dynamics in a population model with mobile and stationary states under a changing environment, which is modeled by a partially degenerate reaction–diffusion equation with a moving variable <span><math><mrow><mi>x</mi><mo>+</mo><mi>c</mi><mi>t</mi></mrow></math></span>, <span><math><mrow><mi>c</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. We focus on whether the species could keep up with the changing environment, that is, whether the equation model has a forced traveling wave with speed <span><math><mi>c</mi></math></span>, and how the switching rates between mobile and stationary states affect the propagation dynamics. It is shown that there exists a threshold value <span><math><mrow><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>></mo><mn>0</mn></mrow></math></span>, such that the equation model admits a forced traveling wave with speed <span><math><mi>c</mi></math></span> if and only if the environment shifting speed <span><math><mrow><mi>c</mi><mo>></mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Thereby, the species cannot follow the changing environment with speed <span><math><mi>c</mi></math></span> if <span><math><mrow><mi>c</mi><mo>≤</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Compared to the well-known results on the classic Fisher’s equation which assumes the population has only mobile state, our result highlights a significant observation: the presence of stationary state in population will reduce the invasion threshold value <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. Moreover, it is proved that such a forced traveling wave is unique and globally stable if <span><math><mrow><mi>c</mi><mo>></mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. This implies that the species can successfully invade new environment as a forced wave if the environment shifting speed <span><math><mi>c</mi></math></span> satisfies <span><math><mrow><mi>c</mi><mo>></mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Some numerical simulations are also provided to illustrate the theoretical results and explain the invasion phenomena of species under environmental changes.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135018"},"PeriodicalIF":2.9,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-04DOI: 10.1016/j.physd.2025.135010
Rossella Della Marca , Alberto d’Onofrio , Carmelo F. Munafò , Romina Travaglini
In this work, in the context of a spatiotemporal Susceptible–Infectious–Removed (SIR) model with vaccination across all-ages, we consider the synergy between vaccine hesitancy and the intrinsic nonlocal spatial and temporal nature of the information used by agents to make their decisions.
First, we analytically investigate the stability of the spatially homogeneous endemic equilibrium: we prove that the proposed model has either Hopf instability or Turing instability, but it cannot have Turing–Hopf instability.
Second, we numerically show that, in the presence of both spatial and temporal nonlocality, the model may exhibit spatiotemporal quasi-periodicity. This phenomenon, to the best of our knowledge, was never been observed before in the context of behavioural epidemiology of infectious diseases. In other cases, instead, the triggering of other interesting spatiotemporal patterns is observed.
{"title":"Spatiotemporal quasiperiodicity induced by all-ages vaccine hesitancy in an SIR model","authors":"Rossella Della Marca , Alberto d’Onofrio , Carmelo F. Munafò , Romina Travaglini","doi":"10.1016/j.physd.2025.135010","DOIUrl":"10.1016/j.physd.2025.135010","url":null,"abstract":"<div><div>In this work, in the context of a spatiotemporal Susceptible–Infectious–Removed (SIR) model with vaccination across all-ages, we consider the synergy between vaccine hesitancy and the intrinsic nonlocal spatial and temporal nature of the information used by agents to make their decisions.</div><div>First, we analytically investigate the stability of the spatially homogeneous endemic equilibrium: we prove that the proposed model has either Hopf instability or Turing instability, but it cannot have Turing–Hopf instability.</div><div>Second, we numerically show that, in the presence of both spatial and temporal nonlocality, the model may exhibit spatiotemporal quasi-periodicity. This phenomenon, to the best of our knowledge, was never been observed before in the context of behavioural epidemiology of infectious diseases. In other cases, instead, the triggering of other interesting spatiotemporal patterns is observed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135010"},"PeriodicalIF":2.9,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-03DOI: 10.1016/j.physd.2025.135014
Hiroki Ono, Yusuke Doi, Akihiro Nakatani
We propose a novel type of umklapp-free lattice (UFL), where umklapp processes are completely absent. The proposed UFL incorporates cubic long-range nonlinearity, a feature not addressed in previous studies. In this paper, we derive an analytical expression for the cubic nonlinear coupling constants by imposing mathematical conditions such that the nonlinear coupling strength between particle pairs decays inversely with their separation distance. The absence of umklapp processes in the proposed lattice is confirmed through numerical comparisons with the Fermi–Pasta–Ulam–Tsingou (FPUT) lattice. Furthermore, molecular dynamics simulations are performed to investigate the thermal conductivity of the proposed lattice in the non-equilibrium steady state. Compared to the original FPUT lattice, the proposed UFL is closer to ballistic transport. Our results demonstrate that the umklapp processes induced by cubic nonlinearity are suppressed in the proposed UFL. Moreover, compared to the UFL with only quartic nonlinearity, truncation of long-range interactions plays a significant role in the proposed lattice.
{"title":"Construction of cubic nonlinear lattice free from umklapp processes","authors":"Hiroki Ono, Yusuke Doi, Akihiro Nakatani","doi":"10.1016/j.physd.2025.135014","DOIUrl":"10.1016/j.physd.2025.135014","url":null,"abstract":"<div><div>We propose a novel type of umklapp-free lattice (UFL), where umklapp processes are completely absent. The proposed UFL incorporates cubic long-range nonlinearity, a feature not addressed in previous studies. In this paper, we derive an analytical expression for the cubic nonlinear coupling constants by imposing mathematical conditions such that the nonlinear coupling strength between particle pairs decays inversely with their separation distance. The absence of umklapp processes in the proposed lattice is confirmed through numerical comparisons with the Fermi–Pasta–Ulam–Tsingou (FPUT) lattice. Furthermore, molecular dynamics simulations are performed to investigate the thermal conductivity of the proposed lattice in the non-equilibrium steady state. Compared to the original FPUT lattice, the proposed UFL is closer to ballistic transport. Our results demonstrate that the umklapp processes induced by cubic nonlinearity are suppressed in the proposed UFL. Moreover, compared to the UFL with only quartic nonlinearity, truncation of long-range interactions plays a significant role in the proposed lattice.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135014"},"PeriodicalIF":2.9,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.physd.2025.135015
Yi Hu, Jiang Yu
Piecewise systems are widely used to model real-world phenomena such as electrical circuits and neurons. Their rich dynamical behavior arises from two factors: the nonlinearity of the subsystems and the nonsmoothness induced by the switching curves. This article focuses on the latter factor. In particular, we consider an extended version of weak Hilbert’s 16th problem for some planar piecewise Hamiltonian systems. In these systems, the subsystems have fixed Hamiltonians, while the switching curves are perturbed in the family of curves. These systems reveal the exclusive influence of the switching curves. To study the influence, we provide the formula of the first order Melnikov function corresponding to the family of -crossing closed orbits and apply it to two problems.
In the first application, we investigate a system with linear subsystems and an algebraic switching curve of order , and prove that such systems have at least limit cycles. This improves the results of Douglas D. Novaes published in Physica D.
In the second application, we study a piecewise linear system with two subsystems and a hyperbola switching curve, and prove the existence of three crossing limit cycles that intersect the switching curve four times.
分段系统被广泛用于模拟现实世界的现象，如电路和神经元。其丰富的动力学行为源于两个因素：子系统的非线性和切换曲线引起的非光滑性。本文主要讨论后一个因素。特别地，我们考虑了一些平面分段哈密顿系统的弱Hilbert第16问题的扩展版本。在这些系统中，子系统具有固定的C1哈密顿量，而开关曲线在C1曲线族中是摄动的。这些系统揭示了开关曲线的独家影响。为了研究这种影响，我们给出了k交叉闭轨道族对应的一阶Melnikov函数的表达式，并将其应用于两个问题。在第一个应用中，我们研究了一个具有线性子系统和n阶代数切换曲线的系统，并证明了这样的系统至少有n个⌊n2⌋极限环。这改进了Douglas D. Novaes发表在《physics d》上的结果。在第二个应用中，我们研究了一个具有两个子系统和双曲线切换曲线的分段线性系统，并证明了与切换曲线相交四次的三个交叉极限环的存在性。
{"title":"Melnikov function of planar piecewise systems with a switching curve perturbed and its applications","authors":"Yi Hu, Jiang Yu","doi":"10.1016/j.physd.2025.135015","DOIUrl":"10.1016/j.physd.2025.135015","url":null,"abstract":"<div><div>Piecewise systems are widely used to model real-world phenomena such as electrical circuits and neurons. Their rich dynamical behavior arises from two factors: the nonlinearity of the subsystems and the nonsmoothness induced by the switching curves. This article focuses on the latter factor. In particular, we consider an extended version of weak Hilbert’s 16th problem for some planar piecewise Hamiltonian systems. In these systems, the subsystems have fixed <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> Hamiltonians, while the switching curves are perturbed in the family of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> curves. These systems reveal the exclusive influence of the switching curves. To study the influence, we provide the formula of the first order Melnikov function corresponding to the family of <span><math><mi>k</mi></math></span>-crossing closed orbits and apply it to two problems.</div><div>In the first application, we investigate a system with linear subsystems and an algebraic switching curve of order <span><math><mi>n</mi></math></span>, and prove that such systems have at least <span><math><mrow><mi>n</mi><mrow><mo>⌊</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></mrow></mrow></math></span> limit cycles. This improves the results of Douglas D. Novaes published in Physica D.</div><div>In the second application, we study a piecewise linear system with two subsystems and a hyperbola switching curve, and prove the existence of three crossing limit cycles that intersect the switching curve four times.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135015"},"PeriodicalIF":2.9,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475984","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 : 2025-10-31DOI: 10.1016/j.physd.2025.135012
Andrea Staino , Frank Gaitan , Biswajit Basu
Solitons are stable, localized solitary waves that can traverse a medium keeping their shape and speed without dissipating or diffusing. The soliton is a paramount concept in nonlinear science and it has been the subject of extensive research in physics. Experiments involving solitons have been conducted in multiple domains, including nonlinear optics, plasma physics, condensed matter, fluid mechanics, information coding and transmission. Designing experiments involving solitons often relies heavily on numerical simulations for predicting system behaviour and optimizing experimental parameters. These simulations require the resolution of nonlinear partial differential equations (PDEs), which are not solvable analytically in most realistic scenarios. On the other hand, numerical resolution of nonlinear PDEs can be computationally challenging, to accurately capture soliton dynamics, interaction effects and long-term stability regimes. Hence, constructing a quantum algorithm for soliton propagation that provides a computational speedup is of great interest. A recent quantum algorithm that solves nonlinear PDEs has been established in the literature. This algorithm has been proven to offer a quadratic speedup for Navier–Stokes and Burgers’ equations. In the present paper the capability of the gradient-free quantum solver to generate soliton solutions is studied. To verify the algorithm, single- and multi-soliton solutions of the well-known Korteweg–de Vries (KdV) equation are considered. First, the reliability of the quantum solver is investigated by comparing the solitary wave obtained from the numerical integration of the KdV with the corresponding analytical solution. Subsequently, the quantum-enabled emergence of solitons from different initial profiles as well as the recovery of known collision properties of classical solitons are examined. Results of numerical simulation of the quantum algorithm are compared with exact solutions and with a classical solver and excellent agreement is found.
{"title":"Classical-quantum simulation of single and multiple solitons generated from the KdV equation","authors":"Andrea Staino , Frank Gaitan , Biswajit Basu","doi":"10.1016/j.physd.2025.135012","DOIUrl":"10.1016/j.physd.2025.135012","url":null,"abstract":"<div><div>Solitons are stable, localized solitary waves that can traverse a medium keeping their shape and speed without dissipating or diffusing. The soliton is a paramount concept in nonlinear science and it has been the subject of extensive research in physics. Experiments involving solitons have been conducted in multiple domains, including nonlinear optics, plasma physics, condensed matter, fluid mechanics, information coding and transmission. Designing experiments involving solitons often relies heavily on numerical simulations for predicting system behaviour and optimizing experimental parameters. These simulations require the resolution of nonlinear partial differential equations (PDEs), which are not solvable analytically in most realistic scenarios. On the other hand, numerical resolution of nonlinear PDEs can be computationally challenging, to accurately capture soliton dynamics, interaction effects and long-term stability regimes. Hence, constructing a quantum algorithm for soliton propagation that provides a computational speedup is of great interest. A recent quantum algorithm that solves nonlinear PDEs has been established in the literature. This algorithm has been proven to offer a quadratic speedup for Navier–Stokes and Burgers’ equations. In the present paper the capability of the gradient-free quantum solver to generate soliton solutions is studied. To verify the algorithm, single- and multi-soliton solutions of the well-known Korteweg–de Vries (KdV) equation are considered. First, the reliability of the quantum solver is investigated by comparing the solitary wave obtained from the numerical integration of the KdV with the corresponding analytical solution. Subsequently, the quantum-enabled emergence of solitons from different initial profiles as well as the recovery of known collision properties of classical solitons are examined. Results of numerical simulation of the quantum algorithm are compared with exact solutions and with a classical solver and excellent agreement is found.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135012"},"PeriodicalIF":2.9,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475982","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 : 2025-10-31DOI: 10.1016/j.physd.2025.135013
Di Qi , Jian-Guo Liu
We present a new strategy for the statistical forecasts of multiscale nonlinear systems involving non-Gaussian probability distributions with the help of observation data from leading-order moments. A stochastic-statistical modeling framework is designed to enable systematic theoretical analysis and support efficient numerical simulations. The nonlinear coupling structures of the explicit stochastic and statistical equations are exploited to develop a new multiscale filtering system using statistical observation data, which is represented by an infinite-dimensional Kalman–Bucy filter satisfying conditional Gaussian dynamics. To facilitate practical implementation, a finite-dimensional stochastic filtering model is proposed that approximates the intractable infinite-dimensional filter solution. We prove that this approximating filter effectively captures key non-Gaussian features, demonstrating consistent statistics with the optimal filter first in its analysis step update, then at the long-time limit guaranteeing stable convergence to the optimal filter. Finally, we build a practical ensemble filter algorithm based on the stochastic filtering model. Robust performance of the modeling and filtering strategies is demonstrated on prototype models, implying wider applications on challenging problems in statistical prediction and uncertainty quantification of multiscale turbulent states.
{"title":"Coupled stochastic-statistical equations for filtering multiscale turbulent systems","authors":"Di Qi , Jian-Guo Liu","doi":"10.1016/j.physd.2025.135013","DOIUrl":"10.1016/j.physd.2025.135013","url":null,"abstract":"<div><div>We present a new strategy for the statistical forecasts of multiscale nonlinear systems involving non-Gaussian probability distributions with the help of observation data from leading-order moments. A stochastic-statistical modeling framework is designed to enable systematic theoretical analysis and support efficient numerical simulations. The nonlinear coupling structures of the explicit stochastic and statistical equations are exploited to develop a new multiscale filtering system using statistical observation data, which is represented by an infinite-dimensional Kalman–Bucy filter satisfying conditional Gaussian dynamics. To facilitate practical implementation, a finite-dimensional stochastic filtering model is proposed that approximates the intractable infinite-dimensional filter solution. We prove that this approximating filter effectively captures key non-Gaussian features, demonstrating consistent statistics with the optimal filter first in its analysis step update, then at the long-time limit guaranteeing stable convergence to the optimal filter. Finally, we build a practical ensemble filter algorithm based on the stochastic filtering model. Robust performance of the modeling and filtering strategies is demonstrated on prototype models, implying wider applications on challenging problems in statistical prediction and uncertainty quantification of multiscale turbulent states.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135013"},"PeriodicalIF":2.9,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475983","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 : 2025-10-31DOI: 10.1016/j.physd.2025.135009
Zhenzhen Yang , Huan Liu , Jing Shen
We delve into the inverse scattering transform of the real-valued vector modified Korteweg–de Vries equation, emphasizing the challenges posed by pairs of higher-order poles in the determinant of the transmission coefficient and the enhanced spectral symmetry stemming from real-valued constraints. Utilizing the generalized vector cross product, we formulate an matrix-valued Riemann–Hilbert problem to tackle the complexities inherent in multi-component systems. We subsequently demonstrate the existence and uniqueness of solutions for a singularity-free equivalent problem, adeptly handling the intricacies of multiple poles. In reflectionless cases, we reconstruct multi-pole soliton solutions through a system of linear algebraic equations.
{"title":"Real-valued vector modified Korteweg–de Vries equation: Solitons featuring multiple poles","authors":"Zhenzhen Yang , Huan Liu , Jing Shen","doi":"10.1016/j.physd.2025.135009","DOIUrl":"10.1016/j.physd.2025.135009","url":null,"abstract":"<div><div>We delve into the inverse scattering transform of the real-valued vector modified Korteweg–de Vries equation, emphasizing the challenges posed by <span><math><mi>N</mi></math></span> pairs of higher-order poles in the determinant of the transmission coefficient and the enhanced spectral symmetry stemming from real-valued constraints. Utilizing the generalized vector cross product, we formulate an <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>×</mo><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> matrix-valued Riemann–Hilbert problem to tackle the complexities inherent in multi-component systems. We subsequently demonstrate the existence and uniqueness of solutions for a singularity-free equivalent problem, adeptly handling the intricacies of multiple poles. In reflectionless cases, we reconstruct multi-pole soliton solutions through a system of linear algebraic equations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135009"},"PeriodicalIF":2.9,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475981","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}
To estimate the displacements of physical state variables, the physics principles that govern the state variables must be considered. Technically, for a certain class of state variables, each state variable is associated to a tensor field. Ways displacement maps act on different state variables will then differ according to their associated different tensor field definitions. Displacement procedures can then explicitly ensure the conservation of certain physical quantities (total mass, total vorticity, total kinetic energy, etc.), and a differential-geometry-based optimization formulated. Morphing with the correct physics, it is reasonable to apply the estimated displacement map to unobserved state variables, as long as the displacement maps are strongly correlated. This leads to a new nudging strategy using all-available observations to infer displacements of both observed and unobserved state variables. Using the proposed nudging method before applying ensemble data assimilation, numerical results show improved preservation of the intrinsic structure of underlying physical processes.
{"title":"Alignment of geophysical fields: A differential geometry perspective","authors":"Yicun Zhen , Valentin Resseguier , Bertrand Chapron","doi":"10.1016/j.physd.2025.134997","DOIUrl":"10.1016/j.physd.2025.134997","url":null,"abstract":"<div><div>To estimate the displacements of physical state variables, the physics principles that govern the state variables must be considered. Technically, for a certain class of state variables, each state variable is associated to a tensor field. Ways displacement maps act on different state variables will then differ according to their associated different tensor field definitions. Displacement procedures can then explicitly ensure the conservation of certain physical quantities (total mass, total vorticity, total kinetic energy, etc.), and a differential-geometry-based optimization formulated. Morphing with the correct physics, it is reasonable to apply the estimated displacement map to unobserved state variables, as long as the displacement maps are strongly correlated. This leads to a new nudging strategy using all-available observations to infer displacements of both observed and unobserved state variables. Using the proposed nudging method before applying ensemble data assimilation, numerical results show improved preservation of the intrinsic structure of underlying physical processes.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134997"},"PeriodicalIF":2.9,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416424","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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