一类新型浅水波方程的2-孤子解  

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

作　　者：居琳[1] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003

出　　处：《山东大学学报（理学版）》2010年第11期93-99,共7页Journal of Shandong University(Natural Science)

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。Two-soliton solutions are studied for a new nonlinear dispersive shallow water wave equations, named Dull- in-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 solu- tion 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 non- linear interaction.

关 键 词：DGH方程 2-孤子解 散射数据 反散射方法 

分 类 号：O175.24[理学—数学]