KdV-Burgers-type Equation and Its Wave Solutions

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

    In this talk, we start with Burgers-type equations, and then focus on the KdV-Burgers-Kuramoto equation, a partial differential equation that occupies a prominent position in describing some physical processes in motion of turbulence and other unstable process systems. Equivalence transformations are applied for exploring the principal Lie symmetry. By means of the associated equivalence algebra and the Preller-Singer procedure, we convert partial differential equations into an overdetermined system from which some explicit and implicit wave solutions are derived in terms of elliptic functions. Numerical simulations of wave phenomena are illustrated, which provide us rich dynamic information.