Influence of Nonlinear Terms on Orbital Stability of Solitary Wave Solutions to the Generalized Symmetric Regularized-Long-Wave Equation

Abstract

The influence of two nonlinear terms on the orbital stability of solitary wave solutions to the generalized symmetric regularized-long-wave(gsrlw) equation is investigated in this paper. Based on the general conclusion to judge the orbit stability of solitary wave solution to the equation, the stable and unstable wave velocity intervals of solitary wave solutions to the gsrlw equation with two low order nonlinear terms are given. By appropriate transformation and scaling, the complexity caused by two high-order nonlinear terms is overcome, and the stable and unstable wave velocity intervals of solitary wave solutions to the gsrlw equation with high-order nonlinear terms are also obtained. Last, the influences of the coefficients and the order of the nonlinear terms on the stability of solitary wave solutions are studied.