Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber

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 Theorem taking advantage that the corresponding standing wave equations can be rewritten a...

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Bibliographic Details
Published in:Revista colombiana de matemáticas 2019, Vol.53 (1), p.87-107
Main Authors: Pipicano, Felipe Alexander, Muñoz Grajales, Juan Carlos
Format: Article
Language:eng ; por
Subjects:
MATHEMATICS
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Summary: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 Theorem 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.
ISSN:0034-7426
2357-4100
DOI:10.15446/recolma.v53n1.81045