中科院数学与系统科学研究院

数学研究所

学术报告会

报告人：Prof. Zhaosheng Feng(University of Texas-Rio Grande Valley, USA)

题  目：Wave Solutions to the Kuramoto-Sivashinsky equation

时  间：2017.06.15（星期四），11:00-12:00

地  点：数学院南楼N913室

摘  要：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.