Publicado

2019-01-01

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

Existencia de soluciones periódicas de onda estacionaria para un sistema que describe la propagación de pulsos en una fibra óptica

DOI:

https://doi.org/10.15446/recolma.v53n1.81045

Palabras clave:

Schrödinger equations, standing wave solutions, nonlinear optics, spectral scheme (en)
Ecuaciones Schrödinger, soluciones de onda estacionaria, óptica no lineal, esquema espectral (es)

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Autores/as

  • Felipe Alexander Pipicano Universidad del Valle - Facultad de Ciencias - Departamento de Matemáticas
  • Juan Carlos Muñoz Grajales Universidad del Valle - Facultad de Ciencias - Departamento de Matemáticas
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.
Establecemos existencia de soluciones estacionarias periódicas para un modelo que describe la propagación de un pulso de luz en el interior de una fibra óptica teniendo en cuenta el efecto Kerr. Para este fin, aplicamos el Teorema Central de Lyapunov tomando ventaja de que las correspondientes ecuaciones de onda estacionaria pueden escribirse como un sistema Hamiltoniano. Además, algunas de estas soluciones son aproximadas usando una iteración de tipo Newton, combinada con un estrategia colocación-espectral para discretizar el sistema de ecuaciones de onda estacionaria. Las simulaciones numéricas presentadas se encuentran de acuerdo con nuestros resultados analíticos.

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Cómo citar

APA

Pipicano, F. A. y Muñoz Grajales, J. C. (2019). Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber. Revista Colombiana de Matemáticas, 53(1), 87–107. https://doi.org/10.15446/recolma.v53n1.81045

ACM

[1]
Pipicano, F.A. y Muñoz Grajales, J.C. 2019. Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber. Revista Colombiana de Matemáticas. 53, 1 (ene. 2019), 87–107. DOI:https://doi.org/10.15446/recolma.v53n1.81045.

ACS

(1)
Pipicano, F. A.; Muñoz Grajales, J. C. Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber. rev.colomb.mat 2019, 53, 87-107.

ABNT

PIPICANO, F. A.; MUÑOZ GRAJALES, J. C. Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. 1, p. 87–107, 2019. DOI: 10.15446/recolma.v53n1.81045. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/81045. Acesso em: 29 may. 2024.

Chicago

Pipicano, Felipe Alexander, y Juan Carlos Muñoz Grajales. 2019. «Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber». Revista Colombiana De Matemáticas 53 (1):87-107. https://doi.org/10.15446/recolma.v53n1.81045.

Harvard

Pipicano, F. A. y Muñoz Grajales, J. C. (2019) «Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber», Revista Colombiana de Matemáticas, 53(1), pp. 87–107. doi: 10.15446/recolma.v53n1.81045.

IEEE

[1]
F. A. Pipicano y J. C. Muñoz Grajales, «Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber», rev.colomb.mat, vol. 53, n.º 1, pp. 87–107, ene. 2019.

MLA

Pipicano, F. A., y J. C. Muñoz Grajales. «Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber». Revista Colombiana de Matemáticas, vol. 53, n.º 1, enero de 2019, pp. 87-107, doi:10.15446/recolma.v53n1.81045.

Turabian

Pipicano, Felipe Alexander, y Juan Carlos Muñoz Grajales. «Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber». Revista Colombiana de Matemáticas 53, no. 1 (enero 1, 2019): 87–107. Accedido mayo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/81045.

Vancouver

1.
Pipicano FA, Muñoz Grajales JC. Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber. rev.colomb.mat [Internet]. 1 de enero de 2019 [citado 29 de mayo de 2024];53(1):87-107. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/81045

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