ScholarLens Back to search
2009•International Journal of Modern Physics BRequires access

N-SOLITON SOLUTIONS, AUTO-BÄCKLUND TRANSFORMATIONS AND LAX PAIR FOR A NONISOSPECTRAL AND VARIABLE-COEFFICIENT KORTEWEG-DE VRIES EQUATION VIA SYMBOLIC COMPUTATION

Lili Li, Bo Tian, Chunyi Zhang, Hai-Qiang Zhang, Juan Li, Tao Xu

Open publisher page 4 citations

Abstract

In this paper, a nonisospectral and variable-coefficient Korteweg-de Vries equation is investigated based on the ideas of the variable-coefficient balancing-act method and Hirota method. Via symbolic computation, we obtain the analytic N-soliton solutions, variable-coefficient bilinear form, auto-Bäcklund transformations (in both the bilinear form and Lax pair form), Lax pair and nonlinear superposition formula for such an equation in explicit form. Moreover, some figures are plotted to analyze the effects of the variable coefficients on the stabilities and propagation characteristics of the solitonic waves.

About this research paper

What this paper is about

In this paper, a nonisospectral and variable-coefficient Korteweg-de Vries equation is investigated based on the ideas of the variable-coefficient balancing-act method and Hirota method. Via symbolic computation, we obtain the analytic N-soliton solutions, variable-coefficient bilinear form, auto-Bäcklund transformations (in both the bilinear form and Lax pair form), Lax pair and nonlinear superposition formula for such an equation in explicit form. Moreover, some figures are plotted to analyze the effects of the variable coefficients on the stabilities and propagation characteristics of the solitonic waves.

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, a nonisospectral and variable-coefficient Korteweg-de Vries equation is investigated based on the ideas of the variable-coefficient balancing-act method and Hirota method. Via symbolic computation, we obtain the analytic N-soliton solutions, variable-coefficient bilinear form, auto-Bäcklund transformations (in both the bilinear form and Lax pair form), Lax pair and nonlinear superposition formula for such an equation in explicit form. Moreover, some figures are plotted to analyze the effects of the variable coefficients on the stabilities and propagation characteristics of the solitonic waves.

Key concepts: Variable coefficient, Lax pair, Korteweg–de Vries equation, Soliton, Variable (mathematics), Bell polynomials, Bilinear interpolation, Mathematics

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
N-SOLITON SOLUTIONS, AUTO-BÄCKLUND TRANSFORMATIONS AND LAX PAIR FOR A NONISOSPECTRAL AND VARIABLE-COEFFICIENT KORTEWEG-DE VRIES EQUATION VIA SYMBOLIC COMPUTATION — Research Paper | ScholarLens