On the Instability of a Class of Periodic Travelling Wave Solutions of the Modified Boussinesq Equation

摘要

This paper is concerned with instability of periodic travelling wave solutions of the modified Boussinesq equation. Periodic travelling wave solutions with a fixed fundamental periodLwill be constructed by using Jacobi's elliptic functions. It will be shown that these solutions, calleddnoidalwaves, are nonlinearly unstable in the energy space for a range of their speeds of propagation andperiods.