具有高阶非线性项的广义二维KdV-Burgers方程的精确解

摘要

The auxiliary equations method is adopted to investigate the exact solutions of the generalized two-dimensionsl KdV-Burgers equations with higher order nonlinear terms. Parameters constraint condition of the auxiliary equations is obtained by using the balance method. Then according to the solutions of auxiliary equation, we can find successfully some explicit solutions of this equation. These solutions include triangular function solutions, hyperbolic function solutions and rational function solutions.%采用辅助方程法研究具有高阶非线性项的广义二维KdV-Burgers方程的精确解,利用平衡法获得了辅助方程的参数约束条件,再根据辅助方程的解成功地获得了所讨论方程的一系列精确解,包括三角函数解、双曲函数解和有理函数解.