一类（2+1）维非线性扰动方程的孤立子行波摄动解

The Solitary Travelling Wave Perturbation Solution to a Class of (2+1) Dimensions Nonlinear Disturbed Equation

摘要:

用行波变换和摄动理论研究了一类广义高维扰动破裂孤子方程. 首先，通过行波变换，将高维问题简化为一维方程，其次，讨论了对应典型的破裂方程，并利用非线性方程待定系数投射方法得到了它的孤子精确解。再利用摄动方法得到了广义非线性扰动破裂方程的孤立子行波渐近解. 最后，举例讨论了用本方法得到的孤立子渐近解的精度，说明了本方法得到的渐近解简单而有效，便于推广到对其它非线性物理模型的求孤立子渐近解..本文使用的方法具有普遍意义，它还能使用于非线性物理和其他实际问题。

Abstract:

A class of higher dimensions disturbed breaking solitary equation is studied using the travelling wave transformation and perturbation theory. Firstly, from a travelling wave transformation, the higher dimension problem changes to one dimension problem. Next, the corresponding typical breaking equation is considered, and its exact solitary solution is obtained by using the undetermined coefficients projectile method. Then, using the perturbation method, the solitary travelling wave asymptotic solution to a disturbed breaking equation is found. Finely, it illustrate that, the obtained asymptotic solutions are simple and valid by using this method. And In this paper, the method has a universal significance. It also used for nonlinear physics and other physical problems.