Review of the Book Optical Solitons: From Fibers to Photonic Crystals by Yu.S. Kivshar and G.P. Agrawal (Academic, San Diego, 2003); Translation from English Edited by N.N. Rozanov (Fizmatlit, Moscow, 2005)

摘要

Nonlinear waves are one of the fundamental objects of nature. They are observed in hydrodynamics and aerodynamics, condensed matter physics and plasma physics, optics and field theory, chemical reaction kinetics and population dynamics, and nuclear physics and the theory of gravity. All nonlinear wave phenomena can be roughly divided into two classes: waves in dispersive and in dissipative media. Among the waves of the first class, solitons occupy a particular place. The history of investigation of solitons amounts to about 200 years. However, the most important event occurred, probably, in 1965, when N. Zabuski and M. Kruskal established that the Korteweg-de Vries equation, which describes waves in shallow water, has solutions in the form of solitary waves with properties of particles: they retain their shape during propagation and after collisions with each other. This fact gave grounds to refer to such waves as solitons (i.e., solitary wave particles, by analogy with such terms as phonon, photon, electron, magnon, etc.). Over the last 30 years, great progress has been achieved in the study of solitons and related phenomena. Along with experimental investigations, methods of mathematical physics were developed that made it possible to develop the theory of solitons. Now solitons are one of the main objects in many problems of nonlinear wave dynamics. It should be noted that nonlinear optics is a field where all the main features of solitons manifest themselves in full measure. The largest number of publications in this field have been devoted to solitons in optical fibers. These objects were referred to as optical solitons, and this term has found wide application. At the beginning of the decade, it became clear that the few existing reviews did not represent completely the achievements and problems of the entire field of optical solitons. In addition, the concepts and methods developed in this field were finding continuously increasing application in a new field of condensed matter physics: Bose-Einstein condensation of ultracold atoms in a magnetic trap. The need arose for a book to be written that would combine the comprehensiveness of an encyclopedia and the depth of a monograph. The evident complexity of this problem is aggravated by the fact that an ideal solution is unlikely to exist. However, this circumstance did not embarrass the authors of this book--well-known experts in the field of wave optics from the Australian National University (Yu.S. Kivshar) and the Institute of Optics, University of Rochester (G.P. Agrawal). A second edition of the book is planned, a fact indicating its success and importance.