Exploring the behavior of solitons on a desktop personal computer

S. López-Aguayo, J.P. Ochoa-Ricoux and J.C. Gutiérrez-Vega

Photonics and Mathematical Optics Group, Optics Center, Tecnológico de Monterrey, Garza Sada 2501, Monterrey, 64849 México.

Recibido el 26 de enero de 2005; ]]> Aceptado el 7 de abril de 2005.

Abstract

In recent years, there has been a growing interest in studying and applying nonlinear wave equations and their soliton solutions. In this paper we discuss at undergraduate level a simple finite-difference numerical method for solving nonlinear wave equations. This method is applied for studying the striking behavior of the optical solitons. The procedures presented can be reproduced by enthusiastic students and instructor with a minimum of programming experience. We provide a set of interesting problems that could be taken as starting point to numerically explore the solutions of nonlinear wave equations.

Keywords: Soliton; nonlinear differential equations; numerical methods.

Resumen

El interés en el estudio de las ecuaciones de onda no lineales y sus soluciones solitónicas se ha incrementado recientemente. En este artículo estudiamos un método numérico muy simple basado en diferencias finitas para solucionar ecuaciones de onda no lineales. Este método es aplicado en el estudio del comportamiento de los solitones ópticos. Los procedimientos expuestos en este trabajo pueden reproducirse por estudiantes e instructores con un mínimo de experiencia en programación. Adicionalmente, incluimos una lista de problemas que pueden servir como punto de inicio para explorar las interesantes soluciones de las ecuaciones no lineales.

Descriptores: Solitones; ecuaciones diferenciales no lineales; métodos numéricos.

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Acknowledgments

This research was supported by the Consejo Nacional de Ciencia y Tecnología of Mexico grant 42808 and by the Tecnológico de Monterrey Research Chair in Optics grant CAT-007.

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