Resumo

QUINTERO, José R.. A water wave mixed type problem: existence of periodic travelling waves for a 2D Boussinesq system. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2015, vol.39, n.150, pp.6-17. ISSN 0370-3908.

In this paper we establish the existence of periodic travelling waves for a 2D Boussinesq type system in threedimensional water-wave dynamics in the weakly nonlinear long-wave regime. For wave speed |c| > 1 and large surface tension, we are able to characterize these solutions through spatial dynamics by reducing a linearly ill-posed mixed type initial value problem to a center manifold of finite dimension and infinite codimension. We will see that this center manifold contains all globally defined small-amplitude solutions of the travelling wave equation for the Boussinesq system that are periodic in the direction of propagation.

Palavras-chave : periodic travelling waves; center manifold approach; stability.

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