Dullin-Gottwald-Holm方程的散射逼近

Scattering approach for the Dullin-Gottwald-Holm equation

研究了一类新型非线性浅水波方程(Dullin-Gottwald-Holm方程,简称为DGH方程)的散射逼近问题,文章首先通过对与离散谱相对应的特征函数的归一化变形,给出了DGH方程的散射数据;其次利用DGH方程的Lax对和Liouville变换求出了初始位势函数,最终论证了DGH方程的可积性.

Scattering approach theory for a new nonlinear shallow water wave equation named DGH equation（Dullin-Gottwald-Holm equation） was studied.Firstly,the scattering data of DGH equation was explicitly determined by proper normalization constants of the eigenfunctions associated with the discrete spectrum.Secondly,an initial potential,which was adjust to the inverse scattering problem,was obtained on the base of Lax pair of DGH equation and Liouville transform.Finally,an approach was presented to prove the integrability of DGH equation.