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International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 637497, 21 pages
Research Article

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

Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos CEP, 13565-905 São Paulo, Brazil

Received 1 February 2010; Accepted 7 May 2010

Academic Editor: Prabir Daripa

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.


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.