一类具n-孤立子解的不可积方程

A CLASS OF NONINTEGRABLE EQUATIONS WITH N-SOLITON SOLUTIONS

本文将H.Corhille等人的工作推广到n孤子的情形,证明了如下事实:如L是以t,x_1,x_2,…,x_(n-1)为参数的线性微分算子时,则当①L具有适当形式时,LK=K^N有n-孤子解;②给出了L_gK=(K_x)~N的不同形式的n-孤子解(N≥2)。

In this paper, using ansatz method, we get many nonintegrable equations which have n-soliton solutions. In the first part, we give the method how to solve equation L_qK=K^N(N≥2). In the second one, we calculate the equation L_qK=(K_x)~N (N≥2). Where, L is linear differential operator.