深水波浪非线性薛定谔方程及其精确解

Nonlinear Schrdinger equation for deep-water wave and its exact solutions

参考Debnath从一般非线性波浪弥散关系推导得出形式为非线性薛定谔方程的波浪传播方程的方法,从非线性二阶Stokes波深水情况下的弥散关系出发,分析了此具体弥散波浪情况下的非线性薛定谔方程,并利用修正影射法对此波浪方程求解,得到非线性波浪周期精确解,此解在形式上与现有解不同,同时包含了Debnath的解,并在极限条件下可得到波浪的孤立波解。

Debnath derived the nonlinear schrodinger （NLS） equation form from the general form of the nonlinear wave dispersion relation. In this paper, the analysis of the NLS equation bagins from the 2-order Stokes＇ nonlinear deep-water wave dispersion relation. The exact solutions of the nonlinear wave are obtained by using the modified mapping method. As this spe- cialization of this equation, the solutions are different from those that obtain and contain the solutions as Debnath did. At the same time, the solitary solution is obtained in the their limit.