Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation

Jaime Angulo and Jose R. Quintero

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-36

Abstract:

We will study the existence and stability of periodic travelling-wave solutions of the nonlinear one-dimensional Boussinesq-type equation Φ t t − Φ x x + a Φ x x x x − b Φ x x t t + Φ t Φ x x + 2 Φ x Φ x t = 0 . Periodic travelling-wave solutions with an arbitrary fundamental period T 0 will be built by using Jacobian elliptic functions. Stability (orbital) of these solutions by periodic disturbances with period T 0 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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:052020

DOI: 10.1155/2007/52020

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