A water wave mixed type problem: existence of periodic travelling waves for a 2D Boussinesq system

José R. Quintero

Resumen


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

Palabras clave


periodic travelling waves, center manifold approach, stability

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DOI: http://dx.doi.org/10.18257/raccefyn.213

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