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二阶Boussinesq方程的孤立波解
林建国¹, 邱大洪²
1.大连海事大学海洋环境工程学院大连116026;2.大连理工大学海岸与近海工程国家重点实验室大连116024

摘要:

基于同量阶迭代法，在保留同阶项的前提下，对林建国等(1998a)得到的二阶Boussinesq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，扩大了孤立波的适用范围。

关键词: 非线性二阶Boussinesq方程孤立波

DOI：

分类号:

基金项目:国家自然科学基金资助项目，59839330号

SOLITARY WAVE SOLUTION TO SECOND-ORDER BOUSSINESQ EQUATIONS

LIN Jian Guo¹, QIU Da Hong²

1.Institute of Marine Environment,Dalian Maritime University,Dalian,116026;2.State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology Dalian,116024

Abstract:

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.

Key words: Nonlinear, Second-order Boussinesq equations, Solitary wave

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