A note on the stability for Kawahara–KdV type equations

In this paper we establish the nonlinear stability of solitary traveling-wave solutions for the Kawahara–KdV equation u t + u u x + u x x x − γ 1 u x x x x x = 0 , and the modified Kawahara–KdV equation u t + 3 u 2 u x + u x x x − γ 2 u x x x x x = 0 , where γ i ∈ R is a positive number when i = 1 , 2 . The main approach used to determine the stability of solitary traveling waves will be the theory developed by Albert (1992) in [9].