一类新型浅水波方程的2-孤子解

J4 ›› 2010, Vol. 45 ›› Issue (11): 93-99.

一类新型浅水波方程的2-孤子解

居琳

江苏科技大学数理学院, 江苏镇江 212003

收稿日期:2010-01-20 出版日期:2010-11-16 发布日期:2010-11-24
作者简介:居琳(1977-),女,硕士,讲师,研究方向为偏微分方程. Email: julin1126@163.com

The two-soliton solution of a new shallow water wave equation

JU Lin

School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, Jiangsu, China

Received:2010-01-20 Online:2010-11-16 Published:2010-11-24

摘要/Abstract

摘要：

研究了一类含线性和非线性色散项的新型浅水波方程即Dullin-Gottwald-Holm方程(简称为DGH方程)的2-孤子解。利用反散射方法建立了DGH方程的反散射求解方程,在不考虑反射的情况下,利用方程的散射数据,借助于Matlab数学软件,以参数形式给出了DGH方程的2-孤子解。最后给出了几个取特殊值时解的波形图,从而清楚地显示了孤波之间的相互作用。

关键词: DGH方程;2-孤子解;散射数据;反散射方法

Abstract:

Two-soliton solutions are studied for a new nonlinear dispersive shallow water wave equations, named Dullin-Gottwald-Holm equation(i.e. DGH equation). Using the inverse scattering transform method, the inverse scattering solving equation of the DGH equation is established. In the case of reflectionless potentials, the known two-soliton solution in a simple parametric form by using the scattering data of equation and Matlab packages is represented. Finally, a few examples of the two-soliton solution profile are presented, which show the familiar phase shift generated by the nonlinear interaction.

Key words: DGH equation; two-soliton solution; scattering data; the inverse scattering method

居琳. 一类新型浅水波方程的2-孤子解[J]. J4, 2010, 45(11): 93-99.

JU Lin. The two-soliton solution of a new shallow water wave equation[J]. J4, 2010, 45(11): 93-99.

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