高维波动方程的一些新的多孤子解

SOME NEW MULTIPLE SOLITON SOLUTIONS OF HIGH-DIMENSIONAL NONLINEAR WAVE EQUATIONS

利用基方程技术和求解基方程新解的变换公式,求得n+1维非线性波动方程的一些新的多孤子解。Gibbon等人指出:多孤子解的孤子数受到限制,N≤2n+1.然而,本文结果表明,他们的结论是不正确的。孤子数N可以是一个任意正整数。

By using the base equations technique and the transtormation relations to get new solutions of the base equations, we obtain some new multiple soliton solutions of n + 1 dimensional nonlinear wave equations. Gibbon et al. pointed out that the number of the soliton in the multiple soliton solutions is constrainted by N≤2n + 1. However, our result shows that their conclusion is not ture, the number of the soliton N may be an arbitrary positive integer.