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

作　　者：张义丰[1,2] 李瑞杰[1,2] 罗锋[1] 江森汇[2] 

机构地区：[1]河海大学海岸灾害及防护教育部重点实验室,江苏南京210098 [2]河海大学环境海洋实验室,江苏南京210098

出　　处：《水科学进展》2009年第3期361-365,共5页Advances in Water Science

基　　金：国家自然科学基金资助项目(40476039);教育部高等学校博士学科点基金资助项目(20050294009)~~

摘　　要：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.

关 键 词：非线性薛定谔方程 弥散关系 孤立波 JACOBI椭圆函数 

分 类 号：TV139.2[水利工程—水力学及河流动力学]