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High-order numerical method for the derivative nonlinear Schrodinger equation

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International Journal of Modeling, Simulation, and Scientific Computing 2017年第1期8卷 258-270页

作者： Shu-Cun Li Xiang-Gui Li Jun-Jie Cao Wen-Bo Li School of Applied ScienceBeijing Information Science and Technology UniversityBeijing 100192P.R.China

In this work,a fourth-order numerical scheme in space and two second-order numerical schemes in both time and space are proposed for the derivative nonlinear Schrodinger *** verify the mass conservation for the two-level implicit *** influence on the soliton solution by adding a small random perturbation to the initial condition is *** numerical experiments are given to test the accuracy order for different schemes,*** also test the conservative property of mass and Hamiltonian for these schemes from the numerical point of view.

关键词： Derivative nonlinear Schrodinger equation finite difference soliton solution random perturbation

Integrability of auto-B?cklund transformations and solutions of a torqued ABS equation

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Communications in Theoretical Physics 2021年第7期73卷 42-46页

作者： Xueli Wei Peter H van der Kamp Da-jun Zhang Department of Mathematics Shanghai UniversityShanghai 200444China Department of Mathematics and Statistics La Trobe UniversityVictoria 3086Australia

An auto-B?cklund transformation for the quad equation Q1_(1) is considered as a discrete equation,called H2^(a),which is a so called torqued version of *** equations H2^(a) and Q1_(1) compose a consistent cube,from which an auto-B?cklund transformation and a Lax pair for H2^(a) are *** generally it is shown that auto-B?cklund transformations admit auto-Backlund *** the auto-Backlund transformation for H2^(a)we derive a seed solution and a one-soliton *** this solution it is seen that H2^(a) is a semi-autonomous lattice equation,as the spacing parameter q depends on m but it disappears from the plane wave factor.

关键词： auto-Bocklund transformation consistency Lax pair soliton solution torqued ABS equation semi-autonomous

A Simplified Hirota Method and Its Application

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Journal of Shanghai University(English Edition) 2003年第2期7卷 143-147页

作者：徐桂琼张善卿李志斌 CollegeofInternationalBusinessandAdministration DepartmentofComputerScience

By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.

关键词： the homogeneous balance principle,simplified Hirota method soliton solution the breaking soliton equation.

Exact solutions for the mixed AKNS equation： Hirota approach

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Journal of Shanghai University(English Edition) 2007年第3期11卷 241-244页

作者：郝宏海吕丽丽 Department of Mathematics College of Sciences Shanghai University Shanghai 200444 P. R. China

The mixed AKNS nonlinear evolution equation in equation, which contains an isospectral term the AKNS system. So searching for its exact and a nonisospectral term, is an important solutions is vital both for the AKNS system and in mathematical sense. In this paper, the corresponding Lax pair was given, the bilinear forms of the mixed AKNS equation were obtained through introducing the transformation of dependent variables. By using Hirota＇s bilinear method, the N-soliton solutions were obtained.

关键词： bilinear form Lax pair Hirota's method soliton solution

soliton and rogue wave solutions of two-component nonlinear Schr?dinger equation coupled to the Boussinesq equation

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Chinese Physics B 2017年第10期26卷 28-37页

作者：宋彩芹肖冬梅朱佐农 School of Mathematical Sciences Shanghai Jiao Tong University

The nonlinear Schrodinger （NLS） equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright-bright, bright-dark, and dark-dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright-bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright-bright or bright-dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.

关键词： multi-component NLS-Boussinesq equation soliton solution rogue wave solution

Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length

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Chinese Physics B 2006年第10期15卷 2216-2222页

作者：李画眉 Department of Physics Zhejiang Normal University Jinhua 321004 China

The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.

关键词： Gross-Pitaevskii equation soliton solution time-dependent atomic scattering length,extended hyperbolic function method

Bilinear Bcklund transformation and explicit solutions for a nonlinear evolution equation

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Chinese Physics B 2010年第4期19卷 37-41页

作者：吴勇旗 Mathematics and Computational Science School Zhanjiang Normal University

The bilinear form of two nonlinear evolution equations are derived by using Hirota derivative. The Backlund transformation based on the Hirota bilinear method for these two equations are presented, respectively. As an application, the explicit solutions including soliton and stationary rational solutions for these two equations are obtained.

关键词： Hirota method Backlund transformation soliton solution

Derivation of Lagrangian density for the“good”Boussinesq equation and multisymplectic disretizations

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Derivation of Lagrangian density for the“good”Boussinesq e...

符号计算与非线性偏微分方程精确行波解(英文)

中国科学院地质与地球物理研究所2008学术年会

作者： Jing-Bo Chen~*,Hong Liu Institute of Geology and Geophysics,Chinese Academy of Sciences,P.O.Box 9825,Beijing 100029,People’s Republic of China

The Lagrangian density for the"good"Boussinesq equation is derived by introducing a new variable in this *** on this density,we consider the corresponding multisymplectic formulation and *** experiments are also repor... 详细信息

关键词： Lagrangian density "Good" Boussinesq equation Multisymplectic soliton solution

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Journal of Shanghai University(English Edition) 2008年第6期12卷 481-485页

作者：吴国成夏铁成 Department of Mathematics College of Sciences Shanghai University Key Laboratory of Mathematics Mechanization Chinese Academy of Science

In this paper, with the aid of the symbolic computation, a further extended tanh function method was presented. Based on the new general ansatz, many nonlinear partial differential equation（s）（NPDE（s）） can he solved. Especially, as applications, a compound KdV-mKdV equation and the Broer-Kaup equations are considered successfully, and many solutions including periodic solutions, triangle solutions, and rational solutions are obtained. The method can also be applied to other NPDEs.

关键词： nonlinear partial differential equations (NPDEs) rational solution soliton solution doubly periodic solution Wu method