Models of shallow water wave equations having peakons, periodic peakons and compactons


主讲人:李继彬 华侨大学教授


地点:腾讯会议 538 474 037



内容介绍:Water waves in channels and oceans are usually described by the Euler equations. Due to their complexity, several approximate models have been derived in various wave regimes. Indeed, considering long waves propagating in shallow water but without assuming small amplitudes, Serre derived a fully nonlinear weakly dispersive system of equations which, with some approximations, include the Korteweg–de Vries, Saint-Venant and Boussinesq equations as special cases. In 2010,Dias and Milewski presented a generalization of the Serre equations, which are fully-nonlinear, weakly dispersive and bidirectional (orisotropic) equations under a built-in assumption of irrotationality. It is very interesting that the corresponding traveling systems of these water wave models are singular traveling wave systems. In this talk, we state how to use the dynamical system approach to study the peakon, periodic peakon and compacton families for these water wave models.