On the Camassa-Holm-KP model arising in shallow water theory
报告人:Professor Yue Liu, University of Texas at Arlington 时间:2020年9月5日9:30
摘要:In this talk we describe the asymptotic perturbation method to derive a two-dimensional Camassa-Holm-Kadomtsev-Petviashvili-type equation in the context of full water waves. Starting from the incompressible and irrotational governing equations in the three-dimensional water waves, we show that such a equation arises in the modeling of the propagation of shallow water waves over a flat bed. The resulting equation is a two dimensional Camassa-Holm equation with weakly transverse effect for the horizontal velocity component. The equation captures stronger nonlinear effects than the classical dispersive integrable equations like the Korteweg-de Vries and Kadomtsev-Petviashvili equations. We also address some properties of the this model equation and how it relates to the surface wave. Finally, we investigate the formation of singularities and the existence of peaked traveling-wave solutions of the model equation.