| Autor: |
Quintero, José Raúl, Grajales, Juan Carlos Muñoz |
| Předmět: |
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| Zdroj: |
Communications on Pure & Applied Analysis; Mar2018, Vol. 17 Issue 2, p557-N.PAG, 22p |
| Abstrakt: |
In this work we establish the existence of at least one weak periodic solution in the spatial directions of a nonlinear system of two coupled differential equations associated with a 2D Boussinesq model which describes the evolution of long water waves with small amplitude under the effect of surface tension. For wave speed 0<|c|<1, the problem is reduced to finding a minimum for the corresponding action integral over a closed convex subset of the space Hk¹(R) (k-periodic functions f∈Lk²(R) such that f′∈Lk²(R)). For wave speed |c|>1, the result is a direct consequence of the Lyapunov Center Theorem since the nonlinear system can be rewritten as a 4×4 system with a special Hamiltonian structure. In the case |c|>1, we also compute numerical approximations of these travelling waves by using a Fourier spectral discretization of the corresponding 1D travelling wave equations and a Newton-type iteration. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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