二阶Boussinesq方程的孤立波解

SOLITARY WAVE SOLUTION TO SECOND-ORDER BOUSSINESQ EQUATIONS

基于同量阶迭代法 ,在保留同阶项的前提下 ,对林建国等 ( 1 998a)得到的二阶Boussi nesq类方程进行求解 ,得到了与其量阶相对应的孤立波解 ,并将其与Euler方程的二阶孤立波解进行了比较 ,结果显示 ,本文解比传统Boussinesq方程的孤立波解有明显的改善 。

Based on the method of iteration with the same order,the solitary wave solution to Boussinesq equations with the second order nonlinear and dispersive terms has been obtained in this paper. A comparison with the second order solitary wave solution to Euler equations shows that the solution obtained in the present paper is the more reasonable than the solitary wave solution to the traditional Boussinesq equations. The results of the present paper extend the applicable range of the solitary wave,enrich the theory of the marine wave dynamics,and provide the exact initial boundary conditions for solving numerically the second order Boussinesq equations.