arXiv - PHYS - Exactly Solvable and Integrable Systems最新文献_第3页

Noncommutative nonisospectral Toda and Lotka-Volterra lattices, and matrix discrete Painlevé equations 非交换非等谱托达和洛特卡-沃尔特拉晶格，以及矩阵离散潘列维方程

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-11 DOI: arxiv-2407.08486

Anhui Yan, Chunxia Li

引用次数: 0

Action-angle variables for the nonlinear Schrödinger equation on the half-line 半线上非线性薛定谔方程的作用角变量

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-09 DOI: arxiv-2407.06916

Baoqiang Xia

引用次数: 0

A modified Korteweg-de Vries equation soliton gas under the nonzero background 非零背景下修正的科特韦格-德弗里斯方程孤子气体

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-07 DOI: arxiv-2407.05384

Xiaoen Zhang, Liming Ling

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Integrability conditions for Boussinesq type systems Boussinesq 型系统的可积分性条件

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-06-28 DOI: arxiv-2406.19919

Rafael Hernandez Heredero, Vladimir Sokolov

引用次数: 0

Reduction of the Laplace sequence and sine-Gordon type equations 拉普拉斯序列和正弦-戈登方程的还原

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-06-28 DOI: arxiv-2406.19837

K I Faizulina, A R Khakimova

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Exact solution of the nonlinear boson diffusion equation for gluon scattering 胶子散射的非线性玻色子扩散方程的精确解

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-06-16 DOI: arxiv-2406.11017

L. Möhringer, G. Wolschin

引用次数: 0

Inverse scattering transform for the defocusing-defocusing coupled Hirota equations with non-zero boundary conditions: double-pole solutions 具有非零边界条件的散焦-聚焦耦合广田方程的反散射变换：双极解

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-06-12 DOI: arxiv-2406.08189

Peng-Fei Han, Wen-Xiu Ma, Ru-Suo Ye, Yi Zhang

{"title":"Inverse scattering transform for the defocusing-defocusing coupled Hirota equations with non-zero boundary conditions: double-pole solutions","authors":"Peng-Fei Han, Wen-Xiu Ma, Ru-Suo Ye, Yi Zhang","doi":"arxiv-2406.08189","DOIUrl":"https://doi.org/arxiv-2406.08189","url":null,"abstract":"The inverse scattering transform for the defocusing-defocusing coupled Hirota\u0000equations with non-zero boundary conditions at infinity is thoroughly\u0000discussed. We delve into the analytical properties of the Jost eigenfunctions\u0000and scrutinize the characteristics of the scattering coefficients. To enhance\u0000our investigation of the fundamental eigenfunctions, we have derived additional\u0000auxiliary eigenfunctions with the help of the adjoint problem. Two symmetry\u0000conditions are studied to constrain the behavior of the eigenfunctions and\u0000scattering coefficients. Utilizing these symmetries, we precisely delineate the\u0000discrete spectrum and establish the associated symmetries of the scattering\u0000data. By framing the inverse problem within the context of the Riemann-Hilbert\u0000problem, we develop suitable jump conditions to express the eigenfunctions.\u0000Consequently, we deduce the pure soliton solutions from the\u0000defocusing-defocusing coupled Hirota equations, and the double-poles solutions\u0000are provided explicitly for the first time in this work.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"2015 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources 非阿贝尔二维户田晶格和具有自洽源的矩阵正弦-戈登方程

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-06-09 DOI: arxiv-2406.05634

Mengyuan Cui, Chunxia Li

引用次数: 0

Fokas-Lenells Derivative nonlinear Schrödinger equation its associated soliton surfaces and Gaussian curvature Fokas-Lenells 衍生非线性薛定谔方程及其相关孤子面和高斯曲率

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-06-05 DOI: arxiv-2406.03203

Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

{"title":"Fokas-Lenells Derivative nonlinear Schrödinger equation its associated soliton surfaces and Gaussian curvature","authors":"Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy","doi":"arxiv-2406.03203","DOIUrl":"https://doi.org/arxiv-2406.03203","url":null,"abstract":"One of the most important tasks in mathematics and physics is to connect\u0000differential geometry and nonlinear differential equations. In the study of\u0000nonlinear optics, integrable nonlinear differential equations such as the\u0000nonlinear Schr\"odinger equation (NLSE) and higher-order NLSE (HNLSE) play\u0000crucial roles. Because of the medium's balance between dispersion and\u0000nonlinearity, all of these systems display soliton solutions. The soliton\u0000surfaces, or manifolds, connected to these integrable systems hold significance\u0000in numerous areas of mathematics and physics. We examine the use of soliton\u0000theory in differential geometry in this paper. We build the two-dimensional\u0000soliton surface in the three-dimensional Euclidean space by taking into account\u0000the Fokas-Lenells Derivative nonlinear Schr\"odinger equation (also known as\u0000the gauged Fokas-Lenells equation). The same is constructed by us using the\u0000Sym-Tafel formula. The first and second fundamental forms, surface area, and\u0000Gaussian curvature are obtained using a Lax representation of the gauged FLE.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rogue wave patterns associated with Adler--Moser polynomials featuring multiple roots in the nonlinear Schrödinger equation 非线性薛定谔方程中与具有多根特征的阿德勒--莫泽多项式相关的流波模式

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-30 DOI: arxiv-2405.19602

Huian Lin, Liming Ling

{"title":"Rogue wave patterns associated with Adler--Moser polynomials featuring multiple roots in the nonlinear Schrödinger equation","authors":"Huian Lin, Liming Ling","doi":"arxiv-2405.19602","DOIUrl":"https://doi.org/arxiv-2405.19602","url":null,"abstract":"In this work, we analyze the asymptotic behaviors of high-order rogue wave\u0000solutions with multiple large parameters and discover novel rogue wave\u0000patterns, including claw-like, OTR-type, TTR-type, semi-modified TTR-type, and\u0000their modified patterns. A correlation is established between these rogue wave\u0000patterns and the root structures of the Adler--Moser polynomials with multiple\u0000roots. At the positions in the $(x,t)$-plane corresponding to single roots of\u0000the Adler--Moser polynomials, these high-order rogue wave patterns\u0000asymptotically approach first-order rogue waves. At the positions in the\u0000$(x,t)$-plane corresponding to multiple roots of the Adler--Moser polynomials,\u0000these rogue wave patterns asymptotically tend toward lower-order fundamental\u0000rogue waves, dispersed first-order rogue waves, or mixed structures of these\u0000rogue waves. These structures are related to the root structures of special\u0000Adler--Moser polynomials with new free parameters, such as the\u0000Yablonskii--Vorob'ev polynomial hierarchy, among others. Notably, the positions\u0000of the fundamental lower-order rogue waves or mixed structures in these rogue\u0000wave patterns can be controlled freely under specific conditions.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0