Nonlinear stability properties of periodic travelling wave solutions of the classical Korteweg–de Vries and Boussinesq equations

Abstract

This article is concerned with nonlinear stability properties of periodic travelling wave solutions of the classical Korteweg de Vries and Boussinesq equations. Periodic travelling wave solutions with a fixed fundamental period L will be constructed by using Jacobi’s elliptic functions. It will be shown that these solutions, called cnoidal waves, are nonlinearly stable in the respective energy space by periodic disturbances with period L.