Communications in Mathematical Sciences

Volume 10 (2012)

Number 3

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

Pages: 917 – 944

DOI: http://dx.doi.org/10.4310/CMS.2012.v10.n3.a10

Author

Juan Carlos Muñoz Grajales (Departamento de Matemáticas, Universidad del Valle, Cali, Colombia)

Abstract

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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