Copyright © 2010 Lynnyngs Kelly Arruda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with instability of periodic travelling wave solutions of the modified Boussinesq equation. 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 dnoidal waves, are nonlinearly unstable in the energy space for a range of their speeds of propagation and periods.