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数学学院、所系列学术报告(709场):美国德克萨斯大学冯兆生教授

admin 发表于: 2017-06-14 09:17  点击:281

   目:Wave Solutions to the Kuramoto-Sivashinsky equation

    人:美国德克萨斯大学 冯兆生教授

   间:20170616 9:00-10:00 

   点:数学楼一楼报告厅

 

 

     In this talk, we develop a connection between an ordinary differential equation that is cubic in the unknown function, and the Kuramoto-Sivashinsky equation, a partial differential equation that occupies a prominent position in describing some physical processes in motion of turbulence and other unstable process systems. We convert the problem into an equivalent integral equation by using the Abel transformation. By means of the Lie symmetry reduction method and the Maximum Principle, we show that there exist nontrivial bounded solitary wave solutions under certain parametric conditions. Numerical simulations of wave phenomena are illustrated, which provide us rich dynamical information and are in agreement with our theoretical analysis.