Asymptotic stability of kink profile solitary wave solutions for generalized gardner equation with dissipative term

Abstract

In this paper, we study the asymptotic stability of the monotone decreasing kink profile solitary wave solutions of the generalized Gardner equation with dissipative term. Firstly, we obtain the estimation of the first-order and second-order derivatives for monotone decreasing kink profile solitary wave solutions, then by using anti-derivative strategy, with the help of prior estimate and Young inequality, we overcome the difficulties caused by two higher-order nonlinear terms of the equation in the estimation, and prove the asymptotic stability of monotone decreasing kink profile solitary wave solution in the sense of [Formula: see text] norm.