Orbital stability of dn periodic solutions for the generalized symmetric regularized-long-wave equation

摘要

In this paper, the orbital stability of dn periodic solutions for the generalized symmetric regularized-long-wave equation with two nonlinear terms is investigated. First, the existence of dn periodic solution to the equation is obtained. Then, according to the Floquet theory and Lame equation, the spectral properties of corresponding linear operators are given. Last, according to the classical theory of stability, the orbital stability of the dn periodic solution for the generalized symmetric regularized-long-wave equation is proved to be stable under the perturbation of period L.