Completely integrable models of non-linear optics

Details Completely integrable models of non-linear optics Completely integrable models of non-linear optics

2000-12-21

arxiv.org/abs/nlin/0012045v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Latex, 17 pages, no figures, submitted to Pramana J

Scientific paper

10.1007/s12043-001-0008-x

The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency, and parametric interaction of three waves. At the present time there are a number of the theories based on completely integrable systems of equations, which are both generations of the original known models and new ones. The modified Korteweg-de Vries equation, the non- linear Schrodinger equation, the derivative non-linear Schrodinger equation, Sine-Gordon equation, the reduced Maxwell-Bloch equation, Hirota equation, the principal chiral field equations, and the equations of massive Thirring model are gradually putting together a list of soliton equations, which are usually to be found in non-linear optics theory.

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