2017.06.01, Lecture: Wave Solutions to the Kuramoto-Sivashinsky equation

Title: Wave Solutions to the Kuramoto-Sivashinsky equation

Speaker: Prof. Zhaosheng Feng

Department of Mathematics, University of Texas-Rio Grande Valley, Edinburg, TX 78539

Abstract: 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 Preller-Singer procedure, we show that there exist nontrivial bounded 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.