检索结果-南通市图书馆

soliton solution to the complex modified Korteweg–de Vries equation on both zero and nonzero background via the robust inverse scattering method

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2022年第7期74卷 30-40页

作者： Yong Zhang Yanwei Ren Huanhe Dong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China College of Economics and Management Shandong University of Science and TechnologyQingdao 266590China

In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background.Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time t is large, then we give the comparison between the exact solution and the asymptotic solution.

关键词： robust inverse scattering method modified Korteweg-de Vries equation soliton solution rational travelling waves asymptotic analysis

On limit fractional Volterra hierarchies

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2024年第1期76卷 7-16页

作者： Lixiang Zhang Chuanzhong Li School of Mathematics and Statistics Ningbo UniversityNingbo315211China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.

关键词： limit fractional Volterra hierarchy noncommutative limit fractional Volterra hierarchy Darboux transformation soliton solution quasi determinant solution

N-soliton solution of a coupled integrable dispersionless equation

在线全文

学校读者我要写书评

暂无评论

Chinese Physics B 2009年第5期18卷 1780-1786页

作者：扎其劳赵银龙李志斌 Department of Computer Science East China Normal University College of Mathematics Science Inner Mongolia Normal University

A new coupled integrable dispersionless equation is presented by considering a spectral problem. A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems. As an application, the N-soliton solution of the coupled integrable dispersionless equation is explicitly given.

关键词： soliton solution Darboux transformation coupled integrable dispersionless equation

Comments on "Inverse scattering method and soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields"

在线全文

学校读者我要写书评

暂无评论

Chinese Physics B 2011年第2期20卷 70-72页

作者：魏益焕 Department of Physics Bohai University

This paper points out that equations （18a） and （18b） in Ref. [7] [Gao Y J 2008 Chin. Phys. B 17 3574] only possess the solutions M = ργc. So, there does not exist the so-called soliton solution family for the Ei... 详细信息

关键词： matrix potential extended hyperbolic complex soliton solution

THE EXPRESSION OF soliton solution FOR SINE-GORDON EQUATION

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 1992年第6期13卷 533-536页

作者：徐宝智方小卫 Zhejiang University Hangzhou Hangzhou Automatic Institute Hangzhou

In this paper, we study the inverse scattering solution for Sine-Grodon equationA particularly concise expression of the soliton solution is obtained, and the single soliton and double soliton solutions are discussed.

关键词： inverse scattering soliton solution reflection coefficient

Reduced nonlocal integrable mKdV equations of type(-λ, λ) and their exact soliton solutions

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2022年第6期74卷 15-20页

作者： Wen-Xiu Ma Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700United States of America

We conduct two group reductions of the Ablowitz-Kaup-Newell-Segur matrix spectral problems to present a class of novel reduced nonlocal reverse-spacetime integrable modified Korteweg-de Vries equations. One reduction is local, replacing the spectral parameter with its negative and the other is nonlocal, replacing the spectral parameter with itself. Then by taking advantage of distribution of eigenvalues, we generate soliton solutions from the reflectionless Riemann-Hilbert problems, where eigenvalues could equal adjoint eigenvalues.

关键词： nonlocal integrable equation soliton solution Riemann-Hilbert problem

RIEMANN-HILBERT PROBLEMS AND soliton solutionS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2022年第1期42卷 127-140页

作者：马文秀 Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700USA School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.

关键词： matrix spectral problem nonlocal reverse-time integrable equation integrable hierarchy Riemann-Hilbert problem inverse scattering transform soliton solution

THE SASA-SATSUMA EQUATION ON A NON-ZERO BACKGROUND: THE INVERSE SCATTERING TRANSFORM AND MULTI-soliton solutionS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2023年第3期43卷 1045-1080页

作者：温丽丽范恩贵陈勇 School of Mathematical Sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical Practiceand Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghai200241China School of Mathematical Sciences and Key Laboratory for Nonlinear Science Fudan UniversityShanghai200433China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3×3 matrix spectrum problem and a nonzero boundary condition. To circumvent the multi-value of eigenvalues, we introduce a suitable two-sheet Riemann surface to map the original spectral parameter k into a single-valued parameter z. The analyticity of the Jost eigenfunctions and scattering coefficients of the Lax pair for the Sasa-Satsuma equation are analyzed in detail. According to the analyticity of the eigenfunctions and the scattering coefficients, the z-complex plane is divided into four analytic regions of D_(j) : j = 1, 2, 3, 4. Since the second column of Jost eigenfunctions is analytic in D_(j), but in the upper-half or lowerhalf plane, we introduce certain auxiliary eigenfunctions which are necessary for deriving the analytic eigenfunctions in Dj. We find that the eigenfunctions, the scattering coefficients and the auxiliary eigenfunctions all possess three kinds of symmetries;these characterize the distribution of the discrete spectrum. The asymptotic behaviors of eigenfunctions, auxiliary eigenfunctions and scattering coefficients are also systematically derived. Then a matrix Riemann-Hilbert problem with four kinds of jump conditions associated with the problem of nonzero asymptotic boundary conditions is established, from this N-soliton solutions are obtained via the corresponding reconstruction formulae. The reflectionless soliton solutions are explicitly given. As an application of the N-soliton formula, we present three kinds of single-soliton solutions according to the distribution of discrete spectrum.

关键词： Sasa-Satsuma equation nonzero boundary condition auxiliary eigenfunctions Riemann-Hilbert problem soliton solution

■-dressing method for the complex modified KdV equation

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2023年第11期75卷 24-29页

作者： Shuxin Yang Biao Li School of Mathematics and Statistics Ningbo UniversityNingbo 315211China School of Foundation Studies Zhejiang Pharmaceutical UniversityNingbo 315500China

The dressing method based on the 2×2 matrix■-problem is generalized to study the complex modified KdV equation(cmKdV).Through two linear constraint equations,the spatial and time spectral problems related to the cmKdV equation are derived.The gauge equivalence between the cmKdV equation and the Heisenberg chain equation is obtained.Using a recursive operator,a hierarchy of cmKdV with source is proposed.On the basis of the■-equation,the N-solition solutions of the cmKdV equation are obtained by selecting the appropriate spectral transformation matrix.Furthermore,we get explicit one-soliton and two-soliton solutions.

关键词： complex modified KdV equation ■-dressing method Lax pair soliton solution