Sufficient conditions for orbital stability of periodic traveling waves (Q2631717)

The paper addresses the existence and stability of periodic solutions of one-dimensional nonlinear partial differential equations, which may be considered as a generalized form of the Korteweg-de Vies (KdV) equation. Particular equations belonging to this class include equations for the propagation of waves on the surface of shallow water, long internal waves in stratified fluids, ion-acoustic waves in plasmas, etc. Accordingly, the periodic waves addressed in this paper may be considered as a generalization of the well-known cnoidal-wave solutions of the KdV equation. The stability analysis is based on the consideration of energy of the periodic-wave solutions, with the help of the respective Hessian matrix.