广义变系数Kdv-Burgers方程的精确解

Exact Solutions of the General Variable Coefficient Kdv-Burgers Equation

摘要: 本文以广义变系数Kdv-Burgers方程为例，介绍了三辅助微分方程展开法求非线性偏微分方程精确解的具体过程，并且由此得到了该方程的一些三孤子解，这些新的孤子解包含了：双曲函数形式解、三角函数形式解、双曲函数与指数函数混合作用解、三角函数与双曲函数混合作用解，三角函数与有理函数混合作用解等等。由于系数的任意性，使得三辅助方程展开法能够构造更多的变系数偏微分方程的精确解。

Abstract: In this paper, taking the generalized variable coefficient Kdv-Burgers equation as an example, the specific process of solving the exact solution of nonlinear partial differential equation by the ex-pansion method of three auxiliary differential equations is introduced, and some three soliton so-lutions of the equation are obtained. These new soliton solutions include: hyperbolic function form solution, trigonometric function form solution, mixed action solution of hyperbolic function and exponential function, mixed action solution of trigonometric function and hyperbolic function, mixed action solution of trigonometric function and rational function, etc. Because of the arbi-trariness of coefficients, the three auxiliary equations expansion method can construct more exact solutions of partial differential equations with variable coefficients.