摘要
本文用行波变换将vB方程化为常微分方程。而后基于简单方程法,选Bernoulli方程为简单方程,平衡方程(组)中最高次非线性项及最高阶导数从而确定解的级数形式。并将VB方程整理为关于G的多项式,令各项系数为0得到一个代数系统,结合代数解及Bernoulli方程的解则得到VB方程的精确行波解,并给出了解的图像。
We firstly convert VB equation into an ODE by traveling-wave transformation. In this paper, we chooseBernoulli equation as the simple equation, and get the series form of the solutions by considering the homogeneousbalance between the highest order derivatives and highest order nonlinear terms in VB equation. Substituting VBequation into a polynomial of G and equating each coefficient to zero, we obtain a set of algebraic equation.Finally we acquire the exact traveling-wave solution by using the solutions of the algebraic system and that ofBernoulli equation, and then we draw the graph.
