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

主讲人：李继彬 华侨大学教授

时间：2022年12月2日10：00

地点：腾讯会议 538 474 037

举办单位：数理学院

主讲人介绍：李继彬教授是国家级有突出贡献专家,在数学领域有着非常崇高的声望和丰硕的研究成果。曾任四届国家自然科学基金委数学学科评审专家组成员,云南省科学技术委员会常务委员,三届云南省数学会理事长,云南省应用数学研究所副所长,昆明理工大学理学院院长等。他曾主持承担国家自然科学基金重点项目和面上项目等10余项,发表论文220余篇,很多结果被国内外文献广泛应用。出版中英文专著8部,主编教材两本、出版科普书两部。三十余年培养硕士和博士研究生70余人。科研成果曾分别获云南省和浙江省科学技术一等奖。

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.