N-SOLITON-LIKE SOLUTIONS AND BÄCKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION-Reference-Cited by-同舟云学术

N-SOLITON-LIKE SOLUTIONS AND BÄCKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION

Published:2011-02-20 Issue:05 Volume:25 Page:723-733
ISSN:0217-9792
Container-title:International Journal of Modern Physics B
language:en
Short-container-title:Int. J. Mod. Phys. B

Author:

FENG QIAN¹,GAO YI-TIAN¹²,MENG XIANG-HUA³,YU XIN¹,SUN ZHI-YUAN¹,XU TAO³,TIAN BO²³⁴

Affiliation:

1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

3. School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing 100876, China

4. Key Laboratory of Information Photonics and Optical Communications (BUPT), Ministry of Education, P.O. Box 128, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract

A non-isospectral and variable-coefficient modified Korteweg–de Vries (mKdV) equation is investigated in this paper. Starting from the Ablowitz–Kaup–Newell–Segur procedure, the Lax pair is established and the Bäcklund transformation in original variables is also derived. By a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. In addition, the bilinear Bäcklund transformation gives a one-soliton-like solution from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217979211058043

Reference66 articles.

1. Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP Equations

2. Time–space integrable decompositions of nonlinear evolution equations

3. On a class of integrable time-dependent dynamical systems

4. Symbolic calculation in chemistry: Selected examples

5. Comment on “Exact solutions of cylindrical and spherical dust ion acoustic waves” [Phys. Plasmas 10, 4162 (2003)]

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