Physica D: Nonlinear Phenomena最新文献_第6页

Inverse scattering transform for the focusing PT-symmetric nonlinear Schrödinger equation with nonzero boundary conditions: Higher-order poles and multi-soliton solutions

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134466

Chuanxin Xu , Tao Xu , Min Li , Yehui Huang

{"title":"Inverse scattering transform for the focusing PT-symmetric nonlinear Schrödinger equation with nonzero boundary conditions: Higher-order poles and multi-soliton solutions","authors":"Chuanxin Xu , Tao Xu , Min Li , Yehui Huang","doi":"10.1016/j.physd.2024.134466","DOIUrl":"10.1016/j.physd.2024.134466","url":null,"abstract":"<div><div>In this paper, we extend the theory of inverse scattering transform for the focusing PT-symmetric nonlinear Schrödinger equation with nonzero boundary conditions by considering the reciprocals of scattering coefficients have multiple higher-order poles. For the inverse problem with the presence of simple, double and triple poles, we study the pole contributions, trace formulas and reconstruction formulas. On the other hand, we present the general N-soliton solutions in the determinant form for the reflectionless case, and particularly analyze the dynamics of heteroclinic multi-soliton solutions which admit the asymptotic phase difference <span><math><mi>π</mi></math></span> as <span><math><mrow><mi>x</mi><mo>→</mo><mo>±</mo><mi>∞</mi></mrow></math></span>. It turns out that the solutions are nonsingular with a wide range of parameters and can display abundant multi-soliton interactions. The discrete eigenvalues correspond to two different localized waves: one is the conventional soliton exhibiting the dark/antidark profile, the other is the heteroclinic breather-like wave. In addition, the asymptotic solitons associated to the double- or triple-pole eigenvalues are localized in some logarithmical curves, and thus they have the variable velocities with the time dependence of attenuation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134466"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Consensus and bipartite consensus in graphon models for opinion dynamics on the sphere

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134503

Zhengyang Qiao, Yicheng Liu, Xiao Wang

引用次数: 0

Learning governing equations of unobserved states in dynamical systems

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134499

Gevik Grigorian , Sandip V. George , Simon Arridge

引用次数: 0

On the compactness of the support of solitary waves of the complex saturated nonlinear Schrödinger equation and related problems

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134516

Pascal Bégout , Jesús Ildefonso Díaz

{"title":"On the compactness of the support of solitary waves of the complex saturated nonlinear Schrödinger equation and related problems","authors":"Pascal Bégout , Jesús Ildefonso Díaz","doi":"10.1016/j.physd.2024.134516","DOIUrl":"10.1016/j.physd.2024.134516","url":null,"abstract":"<div><div>We study the vectorial stationary Schrödinger equation <span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>a</mi><mspace></mspace><mi>U</mi><mo>+</mo><mi>b</mi><mspace></mspace><mi>u</mi><mo>=</mo><mi>F</mi></mrow></math></span>, with a saturated nonlinearity <span><math><mrow><mi>U</mi><mo>=</mo><mi>u</mi><mo>/</mo><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow></math></span> and with some complex coefficients <span><math><mrow><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>. Besides the existence and uniqueness of solutions for the Dirichlet and Neumann problems, we prove the compactness of the support of the solution, under suitable conditions on <span><math><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow></math></span> and even when the source in the right hand side <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is not vanishing for large values of <span><math><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></math></span>. The proof of the compactness of the support uses a local energy method, given the impossibility of applying the maximum principle. We also consider the associate Schrödinger–Poisson system when coupling with a simple magnetic field. Among other consequences, our results give a rigorous proof of the existence of “solitons with compact support” claimed, without any proof, by several previous authors.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134516"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Response analysis of vibro-impact systems under periodic and random excitations

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134476

Yahui Sun , Joseph Páez Chávez , Yang Liu , Przemysław Perlikowski

{"title":"Response analysis of vibro-impact systems under periodic and random excitations","authors":"Yahui Sun , Joseph Páez Chávez , Yang Liu , Przemysław Perlikowski","doi":"10.1016/j.physd.2024.134476","DOIUrl":"10.1016/j.physd.2024.134476","url":null,"abstract":"<div><div>Uncertainties in factors, such as temperature, humidity, and external loads can significantly impact the performance of vibro-impact systems. Effectively managing these uncertainties is essential to ensure the reliability, safety, and performance of engineering systems in real-world operating conditions. This study presents an efficient and straightforward approach to analyze the response of vibro-impact systems subjected to both periodic and random excitations. The method estimates critical noise intensity levels that lead to dangerous noise-induced bifurcations by utilizing confidence ellipses and the global structure of the deterministic system. Furthermore, the most probable locations for stochastic attractor jumps are identified based on the evolution of the maximum eigenvalue of the stochastic sensitivity function over one period of excitation. The proposed method is validated through the analysis of both single- and two-degree-of-freedom impact oscillators. These findings provide a robust framework for predicting complex dynamic behaviors, thereby enhancing the design and application of vibro-impact systems across various engineering fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134476"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Existence of dark solitons for Kundu–Eckhaus equations

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134522

Ling Pan, Shihui Zhu

引用次数: 0

Inverse scattering transform and the soliton solution of the discrete Ablowitz–Ladik equation

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134517

Yin Li , Meisen Chen

引用次数: 0

Particle transport and finite-size effects in Lorentz channels with finite horizons

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134512

Emilio N.M. Cirillo , Matteo Colangeli , Martin Kröger , Lamberto Rondoni

{"title":"Particle transport and finite-size effects in Lorentz channels with finite horizons","authors":"Emilio N.M. Cirillo , Matteo Colangeli , Martin Kröger , Lamberto Rondoni","doi":"10.1016/j.physd.2024.134512","DOIUrl":"10.1016/j.physd.2024.134512","url":null,"abstract":"<div><div>Particle transport is investigated in a finite-size realization of the classical Lorentz gas model. We consider point particles moving at constant speed in a 2D rectangular strip of finite length, filled with circular scatterers sitting at the vertices of a triangular lattice. Particles are injected at the left boundary with a prescribed rate, undergo specular reflections when colliding with the scatterers and the horizontal boundaries of the channel, and are finally absorbed at the left or the right boundary. Thanks to the equivalence with give Correlated Random Walks, in the finite horizon case, we show that the inverse probability that a particle exits through the right boundary depends linearly on the number of cells in the channel. A non-monotonic behavior of such probability as a function of the density of scatterers is also discussed and traced back analytically to the geometric features of a single trap. This way, we do not refer to asymptotic quantities and we accurately quantify the finite size effects. Our deterministic model provides a microscopic support for a variety of phenomenological laws, <em>e.g.</em> the Darcy’s law for porous media and the Ohm’s law in electronic transport.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134512"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Learning dynamical systems from noisy data with inverse-explicit integrators

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134471

Elena Celledoni , Sølve Eidnes , Håkon Noren Myhr

{"title":"Learning dynamical systems from noisy data with inverse-explicit integrators","authors":"Elena Celledoni , Sølve Eidnes , Håkon Noren Myhr","doi":"10.1016/j.physd.2024.134471","DOIUrl":"10.1016/j.physd.2024.134471","url":null,"abstract":"<div><div>We introduce the mean inverse integrator (MII), a novel approach that improves accuracy when training neural networks to approximate vector fields of dynamical systems using noisy data. This method can be used to average multiple trajectories obtained by numerical integrators such as Runge–Kutta methods. We show that the class of mono-implicit Runge–Kutta methods (MIRK) offers significant advantages when used in connection with MII. When training vector field approximations, explicit expressions for the loss functions are obtained by inserting the training data in the MIRK formulae. This allows the use of symmetric and high-order integrators without requiring the solution of non-linear systems of equations. The combined approach of applying MIRK within MII yields a significantly lower error compared to the plain use of the numerical integrator without averaging the trajectories. This is demonstrated with extensive numerical experiments using data from chaotic and high-dimensional Hamiltonian systems. Additionally, we perform a sensitivity analysis of the loss functions under normally distributed perturbations, providing theoretical support for the favorable performance of MII and symmetric MIRK methods.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134471"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The dynamics of a self-exciting homopolar dynamo system

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134474

Qi Meng, Yulin Zhao

引用次数: 0