Orbital stability of solitary waves for generalized Boussinesq equation with two nonlinear terms

Abstract

This paper investigates the orbital stability and instability of solitary waves for the generalized Boussinesq equation with two nonlinear terms. Firstly, according to the theory of Grillakis–Shatah–Strauss orbital stability, we present the general results to judge orbital stability of the solitary waves. Further, we deduce the explicit expression of discrimination d′′(c) to judge the stability of the two solitary waves, and give the stable wave speed interval. Moreover, we analyze the influence of the interaction between two nonlinear terms on the stable wave speed interval, and give the maximal stable range for the wave speed. Finally, some conclusions are given in this paper.