Odyssey of Light in Nonlinear Optical Fibers

7 Hidden symmetry reductions and the Ablowitz–Kaup–Newell– Segur hierarchies for nonautonomous solitons

V. N. Serkin, A. Hasegawa and T. L. Belyaeva

7.1 Introduction

Nonlinear science is considered to be the most important frontier for understanding nature [1, 2]. The interpenetration of the main ideas and methods being used in different fields of science and technology has become one of the decisive factors in the progress of science as a whole. Among the most spectacular examples of such an interchange of ideas and theoretical methods for analysis of various physical phenomena is the problem of soliton formation.

Solitons—self-localized robust and long-lived nonlinear solitary waves that do not disperse and preserve their identity during ...