Integrability and soliton solutions of a forced extended Korteweg-de Vries equation withvariable coefficients
首发时间:2012-02-07
Abstract:Under investigation is a forced extended Korteweg-deVries (KdV) equation with time- and space-dependent variablecoefficients, which can describe the transcritical flow of astratified fluid over an obstacle. NonisospectralAblowitz-Kaup-Newell-Segur (AKNS) system for this equation isconstructed via the symbolic computation. General integrableconditions are given, under which this equation can be reduced tosuch integrable equations as the KdV and extended KdV equations withvariable coefficients. One- and two- soliton solutions are givenexplicitly through the binary-Bell-polynomial method under theintegrable conditions. Effects of the variable coefficients on thekink-type (kink and antikink) and bell-profile-like (elevation anddepression) solitons are analyzed respectively. Furthermore, typesof soliton interactions are presented with the different choices ofthe variable coefficients.
keywords: Partial differential equation Integrability Solitonsolution Symbolic computation Binary Bell polynomial
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带有外加势的变系数扩展KdV方程的可积性研究和孤子解
摘要:本文研究了带有外加势的变系数扩展KdV方程,它可以用来描述流过障碍物时的分层流体跨临界流。通过计算机符号计算,构造了方程的非等谱的AKNS系统。并给出了广义的可积条件,在这个条件下,该方程可以退化为可积的变系数KdV方程和扩展KdV方程。借助双贝尔多项式方法,在可积条件下获得了方程的单孤子和双孤子解。分析了变系数效应对扭结型和钟形孤子的影响。最后,在不同的变系数条件下给出了几种类型的孤子相互作用情况。
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