El trabajo contiene prácticamente los más diversos aspectos del fenómeno solitónico. Se muestra gradualmente el desarrollo de la teoría moderna de los solitones. Se especula sobre su posible aplicación práctica y se ilustra con ejemplos, los logros recientes en óptica no lineal. Se consideran nuevos métodos de dinámica no lineal que se enlazan con teorías cuánticas, asi como la implicación que los solitones tienen en los escenarios de teoría de campo y de partículas.
This work contains the most important current aspects ofthe soliton phenomena. Starting with a brief history of the scientific appearance of solitons, we explain the most remarkable achievements of the physical and mathematical theory of them which have attracted the attention of physics and mathematics, especially from 70th. We review the setting of several important soliton features an accessible form for easy reading for people who do not possess a special mathematical background. We gradually show the development of the modem soliton theory, more precisely, the remarkably exact methods of solving an unexpected large amount of nonlinear problems. They aim to reveal a deep intemal symmetry inherent integrable models, and also to embed in mathematical physics a modem algebraic geometry specially its great body of methods linked with topology theories. We speculate on possible practical applications and illustrate them through the recent achievements innonlinear optics. New approaches of nonlinear dynamics which connect quantum theory and the fundamental implications that solitons have on the field and particle scenarios are considered.
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