Revisión

A survey of embedded solitons

J. Fujioka, A. Espinosa–Cerón, and R.F. Rodríguez

Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20–364, 1000 D.F., México.

Recibido el 3 de marzo de 2005
Aceptado el 28 de noviembre de 2005

Abstract

At the end of the nineties a brand–new type of soliton was discovered: the embedded solitons. Initially they were found in optical systems, and afterwards they were also found in hydrodynamic models, liquid crystal theory and discrete systems. These peculiar solitary waves are interesting because they exist under conditions in which, until recently, the propagation of solitons was thought to be impossible. At first these nonlinear waves were believed to be necessarily isolated and unstable, but later on it was found that they can be stable and may exist in families. This paper explains what these embedded solitons are, in which models they have been found, and what variants exist (stable, unstable, continuous, discrete, etc.).

Keywords: Embedded solitons; solitary waves; nonlinear waves; liquid crystals; discrete systems.

Resumen

Al final de los noventa se descubrio un nuevo tipo de solitones: los solitones embebidos. Inicialmente estas peculiares ondas se encontraron en sistemas opticos, y posteriormente también se hallaron en modelos hidrodinámicos, en la teoría de cristales líquidos, y en sistemas discretos. Estas ondas solitarias son de interes porque existen en condiciones bajo las cuales, hasta hace poco, se consideraba que era imposible la propagacion de solitones. En un principio se creyó que estas ondas no lineales forzosamente eran soluciones aisladas e inestables, pero más tarde se encontro que pueden ser estables y existir en familias. En este artículo se explica que son estos solitones embebidos, en que modelos han sido hallados, y que variantes existen (estables, inestables, continuos, discretos, etc.).

Descriptores: Solitones embebidos; ondas solitarias; ondas no lineales; cristales líquidos; sistemas discretos.

PACS: 42.65.Tg; 42.81.Dp; 05.45.Yv; 02.30Jr

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Acknowledgements

We wish to thank DGSCA–UNAM (Direccion de Servicios de Computo Académico of UNAM) for their authorization to use their computers Origin 2000 and Bakliz in our study of embedded solitons. The numerical results presented in Refs. 31, 37, 41, and 43 were obtained with the aid of these computers. We also wish to thank the DGAPA–UNAM (Direccion General de Asuntos del Personal Académico of UNAM) for the support received through the PAPIIT project IN112503.

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