On the Scattering Problem for Dullin-Gottwald-Holm Equation

摘要

In this paper studies the scattering problem for new completely integrable dispersive shallow water wave equation, be called Dullin-Gottwald-Holm(DGH) equation. Give its Lax pair, Wronskian antisymmetric bilinear form, get spectral theory of the DGH equation. Result that DGH equation has a global solution, the solitary waves of the equation are solitons, all solitary waves of (2) are stable, the scattering data of the scattering problem for the equation can are expressed.