Title1: Symbolic computation of conservation laws of nonlinear partial differential equations

报告人1：赫尔曼教授, 美国科罗拉多矿业大学

报告时间： 2022年12月16号（星期五）上午： 8:00-9:00

报告地点： 学院20栋306教室 线上：#腾讯会议：103-395-651

Abstract：A method will be presented for the symbolic computation of conservation laws of nonlinear partial differential equations (PDEs) involving multiple space variables and time.Using the scaling symmetries of the PDE, the conserved densities are constructed as linear combinations of scaling homogeneous terms with undetermined coefficients. The variational derivative is used to compute the undetermined coefficients. The homotopy operator is used to invert the divergence operator, leading to the analytic expression of the flux vector. The method is algorithmic and has been implemented in Mathematica. The software is being used to compute conservation laws of nonlinear PDEs occurring in the applied sciences and engineering.The software package will be demonstrated for PDEs that model shallow water waves, ion-acoustic waves in plasmas, sound waves in nonlinear media, and transonic gas flow. Equations featured in this talk include the Korteweg-de Vries and Zakharov-Kuznetsov equations.

简介：赫尔曼教授，美国科罗拉多矿业大学应用数学与统计系荣誉教授，是国际知名的符号计算专家。其研究领域涉及应用数学、微分方程、数学建模、理论力学和符号计算等，特别在在非线性波、孤立子理论、可积性、对称分析、小波分析、数学软件研究方面取得了许多重要的学术成果。曾担任多家国际学术期刊的编委，组织过许多重要的学术会议和活动，主持过多项美国自然科学基金项目的研究。

Title2: Models of shallow water wave equations having peakons, periodic peakons and compactons

报告人2：李继彬教授, 华侨大学

报告时间： 2022年12月16号（星期五）上午： 9:00-10:00

报告地点： 学院20栋306教室 线上：#腾讯会议：103-395-651

Abstract：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.

简介：李继彬，教授，博士生导师，国家级突出贡献专家。主要从事动力系统与非线性微分方程等领域的研究。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250多篇，在“科学出版社”等出版中英文专著10余部，主编教材两部、出版科普书两本。三十余年来培养硕士和博士研究生70余人。曾获国家优秀教学成果二等奖（排名第一），科研成果曾分别获云南省和浙江省科学技术一等奖（排名第一）。

 欢迎数学、物理等专业感兴趣的教师和研究生参加!