耦合非线性波动方程组的约化摄动分析

The reductive perturbation analysis of coupled nonlinear wave equations

基于远方场理论的思想,应用约化摄动分析方法对耦合KdV方程和耦合mKdV方程进行了近似求解,并得到了它们的几组孤立波解,与已有结论相比,其振幅的物理意义更加丰富.在特殊情况下,所得到的近似解与精确解具有完全相同的形式.分析表明,所应用的约化摄动方法在研究小振幅扰动问题方面有一定的普适性.

Based on the far-field theory , the coupled KdV equations and coupled mKdV equations are analysed by using the reductive perturbation analysis method, and some solitary wave solutions are obtained. The amplitude of solitary waves shows more prolific physics signification comparing with the conclusions of existing references. If the waves are damped and inclined zero at infinite farness, the approximate solutions are the same as exact solutions in this paper. It is shown that the reduetive perturbation method will be extensivelv applied in studying the small amplitude disturbance problems.