【摘要】 利用试探函数法,应用到KdV方程和Burgers方程和KdV-Burgers方程化为一个易于求解的代数方程,然后用待定系数法确定相应的常数,可简洁求得一类非线性偏微分方程的精确新解,此方法可望进一步推广用于求解其他非线性偏微分方程。更多还原

【Abstract】 It is not easy to solve the KdV equations,the Burgers equations and KdV-Burgers equations by the usual ways.While by making use of the trial function method,the KdV equations,the Burgers equations and KdV-Burgers equations can be reduced to a set of algebraic equations which can be easily solved,and their related coefficients can be easily determined by the undetermined coefficients method.Then,the new analytical solutions to the KdV equations,the Burgers equations and KdV-Burgers equations can be successfully derived.This method may be generalized to construct the solutions of other nonlinear partial differential equations(PDES for short).更多还原