Abstract

PIPICANO, FELIPE ALEXANDER  and  MUNOZ GRAJALES, JUAN CARLOS. Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber. Rev.colomb.mat. [online]. 2019, vol.53, n.1, pp.87-107. ISSN 0034-7426.

We establish existence of periodic standing waves for a model to describe the propagation of a light pulse inside an optical fiber taking into account the Kerr effect. To this end, we apply the Lyapunov Center Theo-rem taking advantage that the corresponding standing wave equations can be rewritten as a Hamiltonian system. Furthermore, some of these solutions are approximated by using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the system of standing wave equations. Our numerical simulations are found to be in accordance with our analytical results.

Keywords : Schrodinger equations; standing wave solutions; non-linear optics; spectral scheme.

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