Asymptotic Stability of Monotone Decreasing Kink Profile Solitary Wave Solutions for Generalized KdV-Burgers Equation

In this paper, we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation. We obtain the estimate of the firstorder and second-order derivatives for monotone decreasing kink profile solitary wave solutions, and overcome the difficulties caused by high-order nonlinear terms in the generalized KdV-Burgers equation in the estimate by using L2 energy estimating method and Young inequality. We prove that the monotone decreasing kink profile solitary wave solutions are asymptotically stable in H1. Moreover, we obtain the decay rate of the perturbation. in the sense of L2 and L8 norm, respectively, which are (1 + t)- 1/2 and (1 + t)- 1/4 by using Gargliado-Nirenberg inequality.