Existence and computation of periodic travelling-wave solutions of a dispersive system

We establish existence of periodic travelling-wave solutions to a generalized Boussinesq system by using the topological degree theory for positive operators defined on a cone in an appropriate Banach space. Furthermore, we derive a high-accuracy pseudospectral solver based on a Fourier decomposition to construct numerical approximations of these stationary solutions. The numerical simulations are in perfect agreement with the theoretical results and new travelling-wave solutions of the system are computed which do not belong to the family of solutions proved to exist.

Keywords

Boussinesq system, periodic travelling-wave solutions, pseudospectral methods

2010 Mathematics Subject Classification

35Q51, 42A45, 47A75, 76M45

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Published 9 April 2012