一类广义扰动KdV-Burgers方程的同伦近似解

Homotopic approximate solutions for a class of generalized perturbed Kdv-Burgers equation

通过构造一个同伦映射,研究了一类广义扰动KdV-Burgers方程.在引入典型无扰动任意次广义KdV-Burgers方程扭状孤立波解的基础上,研究了扰动方程的具有任意精度的近似解,指出了近似解级数的收敛性,最后利用不动点定理,进一步说明近似解的有效性,并对精度进行了讨论.

A class of generalized disturbed KdV-Burgers equation is studied by constructing a homotopy mapping. Based on the kinked solitary-wave solution of the corresponding typical undisturbed generalized KdV-Burgers equation with nonlinear terms of any or- der, the approximate solution with arbitrary degree of accuracy for the disturbed equation is researched. It is pointed out that the series of approximate solution is convergent. Finally,the efficiency and accuracy of the approximate solutions is also discussed by using the fixed point theorem.