研究了一类由Dullin-Gottwald和Holm提出的新的含线性和非线性色散项的完全可积型浅水波方程(称为Dullin-Gottwald-Holm方程)的反散射问题。首先利用反散射方法建立了DGH方程的反散射方程以及一系列求解方程,并且给出了解的一般形式,然后利用散射数据以参数形式给出了DGH方程的1-孤子解,最后画出了几个取特殊值时解的侧面图。
The inverse scattering problem for the new completely-integrable shallow water wave equation namely Dullin-Gottwald-Holm Equation is studied, in which the linear and nonlinear dispersions are included. The inverse scattering transform method is used to establish the inverse scattering equation of the DGH equation as well as a series of solving equations. The known one-soliton solution in a simple parametric form is obtained by using the scattering data. Some examples of the one-soliton solution are given in the form of profile.