摘要
提出了寻找变系数非线性演化方程精确解的函数展开法,并用该方法找到了变系数Burgers方程、变系数KdV方程和变系数KdV-Burgers方程在一定条件下的精确解,其中包括孤立波解和奇异行波解.一个重要的结果是:当KdV-Burgers方程中系数满足一定条件时,其解由一扭结形孤立波和一钟形孤立波简单迭加而成;在传播过程中,两波速度均随时间变化,扭结形孤立波振幅不变,而钟形孤立波的振幅发生变化.
A function expansion method is presented for solving nonlinear evolution equations with variable coefficients. Many exact solutions including solitary wave solutions and other kind of traveling wave solutions of variable coefficient Burgers equation, variable coefficient KdV equation and variable coefficient KdV-Burgers equation are derived by this method. An important result shows that one of the solutions of KdV-Burgers equation is composed of a kink solitary wave and a bell-like one. As the wave traveling, the amplitude of the kink solitary wave will not change but the bell-like one will change, all their velocities change with time t.
出处
《西北师范大学学报（自然科学版）》
CAS
2005年第5期31-36,共6页
Journal of Northwest Normal University(Natural Science)
基金
国家自然科学基金资助课题(10247008)
