变系数超对称KdV方程的双线性方法

Bilinear Method for the Supersymmetric Variable Coefficient KdV Equation

主要利用双线性方法寻找变系数超对称KdV方程的孤子解。首先通过直接法给出了变系数KdV方程超对称化形式,其次通过适当的变量变换,将非线性方程的Hirota双线性方法和双线性Bcklund变换这两种求解方法变换推广到变系数超对称KdV方程中,利用这两种方法分别求出变系数超对称KdV方程的孤子解的表达形式。

The discussion of integrability of soliton equation is important for soliton theory.The exact solution of a nonlinear soliton equation is another essential aspect in soliton problem.Among them,the Hirota method and Backlund transformation are proved to be the effective approaches to find the exact solutions for the nonlinear soliton equation.In this paper,the supersymmetric form of the variable coefficient Korteweg-de Vries(VCKdV)equation is given.The soliton solutions for the VCKdV equation are derived by Hirota method and Backlund transformation.First,how to seek the supersymmetry VCKdV equation was discussed by the direct method.Through variable transformation and bilinear method,the supersymmetry variable coefficient KdV equation can be written in a bilinear form.Soliton solutions for the supersymmetry VCKdV equation are obtained by supersymmetry bilinear derivatives.Then starting from the bilinear form of the Supersymmetry VCKdV equation,the bilinear Backlund transformation was obtained.By the commutability of the bilinear Backlund transformation,the one soliton solution,two soliton solution,and three soliton solution for the supersymmetry VCKdV equation were given respectively.