构造非线性演化方程精确解新方法

A new approach to construct exact solutions of nonlinear evolution equations

借助于 Mathematica和吴方法 ,运用双曲函数方法 ,获得了一类 Kd V-Burgers和 Kd V方程的多组精确行波解 ,其中包括新的奇性孤波解和新的周期解 .这个算法也可用于解其他的非线性偏微分方程 ,如变更 Boussinesq方程组、非线性浅水长波近似方程组等 .这个算法可以部分地在计算机上完成 .

With the aid of Mathematica and Wu elimination method, several types of explicit and exact travelling wave solutions for a system of KdV Burgers and KdV equations are obtained by hyperbolit function method. These solutions contain new singular solitary and new periodic solutions. The method can also be applied to solve some other systems of nonlinear partial differential equations, such as variant Boussinesq and the nonlinear approximate equations for long wave in shallow water. Some steps of this algorithm can be carried out by computer.