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

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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 ***, 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

N-soliton solution of a coupled integrable dispersionless equation

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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"

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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

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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

A Bilinear Bcklund Transformation and N-soliton-Like solution of Three Coupled Higher-Order Nonlinear Schrdinger Equations with Symbolic Computation

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Communications in Theoretical Physics 2008年第9期50卷 689-695页

作者： ZHU Hong-Wu TIAN Bo MENG Xiang-Hua LI Juan XU Tao School of Science P.O. Box 122 Beijing University of Posts and Telecommunications Beijing 100876 China Key Laboratory of Optical Communication and Lightwave Technologies Ministry of Education Beijing University of Posts and Telecommunications Beijing 100876 China Hunan Meteorological Observatory Changsha 410007 China

A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.

关键词： coupled higher-order nonlinear Schroedinger equations Baecklund transformation soliton solution Wronskian technique symbolic computation

soliton solutions for a Negative Order AKNS Equation Hierarchy

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Communications in Theoretical Physics 2009年第9期52卷 395-397页

作者： JI Jie ZHANG Jian-Bing ZHANG Da-Jun College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China School of Mathematics Science Xuzhou Normal University Xuzhou 221116 China Department of Mathematics Shanghai University Shanghai 200444 China

In this paper,bilinear form of a negative order AKNS equation hierarchy is *** soliton solutionsare obtained through Hiorta's direct method.

关键词： negative order AKNS equation hierarchy Hiorta's direct method soliton solution

soliton solutions for a Negative Order AKNS Equation

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Communications in Theoretical Physics 2008年第11期50卷 1033-1035页

作者： JI Jie ZHAO Song-Lin ZHANG Da-Jun College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China Department of Mathematics Shanghai University Shanghai 200444 China

In this short paper,bilinear form of a negative order AKNS equation is *** N-soliton solutions areobtained through Hiorta's direct method.

关键词： negative order AKNS equation Hiorta's direct method soliton solution

soliton solutionS OF A CLASS OF GENERALIZED NONLINEAR SCHRODINGER EQUATIONS

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Applied Mathematics(A Journal of Chinese Universities) 1997年第4期12卷 389-398页

作者： CAOQINGJIE ZHANGTIANDE K.DJIDJELI G.W.PRice E.H.TWIZELL DepartmentofMathematicsandPhysics ShangdongUniversityofTechnologyJinan.Chlna250061 DepartmentoFMathematicsandPhysics ShangdongUniver.~ityo~Tecl~nologyJinan.China250061 DepartmentofShipScience UniversityofSouthamptonSouthamptonSo171BJEngland. DepartmentofShipScience UniversityofSouthamptonSouthamptonSO171BJEngland DepartmentofMathematicsandStatistics BrunelUniversityUxbridgeMiddlesexUB83PHEngland.

soliton solutions of a class of generalized nonlinear evolution equations are discussed analytically and numerically. This is done by using a travelling wave method to formulate one soliton solution and the finite difference method to the numerical solutions and the interactions between the solitons for the generalized nonlinear Schrdinger equations. The characteristic behavior of the nonlinearity admitted in the system has been investigated and the soliton states of the system in the limit when α→0 and α→∞ have been studied. The results presented show that the soliton phenomenon is characteristics associated with the nonlinearities of the dynamical systems.

关键词： soliton solution generalized nonlinear Schr?dinger equation weighted six-point scheme

N-soliton solutions of an integrable equation studied by Qiao

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Chinese Physics B 2013年第4期22卷 40-45页

作者：扎其劳 College of Mathematics Science Inner Mongolia Normal University

In this paper, we studied N-soliton solutions of a new integrable equation studied by Qiao [J. Math. Phys. 48 082701 （2007）]. Firstly, we employed the Darboux matrix method to construct a Darboux transformation for the modified Korteweg-de Vries equation. Then we use the Darboux transformation and a transformation, introduced by Sakovich [J. Math. Phys. 52 023509 （2011）], to derive N-soliton solutions of the new integrable equation from the seed solution. In particular, the multiple soliton solutions are explicitly obtained and shown through some figures.

关键词： soliton solution Darboux transformation integrable equation