Painleve Analysis and Multi-soliton Solutions for a Variable-coefficient Nonlinear Schrodinger Equation with Symbolic Computation
首发时间:2008-09-28
Abstract:The inhomogeneous variable-coefficient nonlinear Schrodinger equation is hereby under investigation. Painleve analysis leads to the explicit constraint on the variable coefficients for such an equation to pass the Painleve test.With the help of symbolic computation, the bilinear form is obtained through the modified bilinear transformation, and the multi-soliton solutions are given by means of the formal parameter expansion technique.A Backlund transformation in bilinear form is also presented.
keywords: Variable-coefficient nonlinear Schrodinger equation Painleve analysis Backlund transformation Bilinear form;Multi-soliton solution;Symbolic computation
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利用符号计算对变系数Schrodinger方程的进行Painleve分析及求其多孤子解
摘要:本文讨论一个变系数非线性Schrödinger方程. 通过Painlevé分析得到方程通过Painlevé检测时变系数之间的约束条件. 利用修改的双线性变换给出双线性形式,并且利用小参数展开得到方程的孤子解,选择不同的参数描绘出不同的孤子图. 在双线性形式的基础上,双线性形式的Bäcklund变换得以给出.
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利用符号计算对变系数Schrodinger方程的进行Painleve分析及求其多孤子解
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