International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 52020, 36 pages
Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation
1Departamento de Matemática, Instituto de Matemática, Estatística e Computaçäo Científica, (IMECC), UNICAMP, CP 6065, Campinas CEP 13083-970, Säo Paulo, Brazil
2Departamento de Matemáticas, Universidad del Valle, Cali A. A. 25360, Colombia
Received 11 May 2006; Revised 1 October 2006; Accepted 7 February 2007
Academic Editor: Vladimir Mityushev
Copyright © 2007 Jaime Angulo and Jose R. Quintero. 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.
We will study the existence and stability of periodic travelling-wave solutions of the nonlinear one-dimensional Boussinesq-type equation . Periodic travelling-wave solutions with an arbitrary fundamental
period will be built by using Jacobian elliptic functions.
Stability (orbital) of these solutions by periodic disturbances
with period will be a consequence of the general stability criteria given by M. Grillakis, J. Shatah, and W. Strauss. A complete study of the periodic eigenvalue problem associated to the Lame equation is set up.