变系数GKP方程的精确解

Exact solution of GKP equation with variable coefficients

对一类变系数GKP方程求解,首先构造出解的形式并结合不同的辅助方程的新解及相应的Bcklund变换,在数学计算软件的帮助下获得了该方程的无穷序列类孤子新精确解。这些解的类型包括Jacobi椭圆函数型、三角函数型、指数函数型、双曲函数型等。然后又使用假设孤立波方法研究这一类变系数GKP方程,进而得到了另类的孤立波解。

In order to solve a kind of GKP equation with variable coefficients,the form of the solution is first constructed then combined with the newsolutions of different auxiliary equations and corresponding B?cklund transformations. With the help of mathematical calculation software,the newexact solutions of infinite sequence soliton-like of the equation are obtained. The types of these solutions include Jacobi elliptic function type,trigonometric function type,exponential function type,hyperbolic function type,etc.Using the hypothetical solitary wave method,this kind of GKP equation with variable coefficients is studied. Then alternative solitary wave solutions are obtained.