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The idea of devoting a complete book to this topic was born at one
of the Workshops on Nonlinear and Turbulent Processes in Physics
taking place reg ularly in Kiev. With the exception of E. D. Siggia
and N. Ercolani, all authors of this volume were participants at
the third of these workshops. All of them were acquainted with each
other and with each other's work. Yet it seemed to be somewhat of a
discovery that all of them were and are trying to understand the
same problem - the problem of integrability of dynamical systems,
primarily Hamiltonian ones with an infinite number of degrees of
freedom. No doubt that they (or to be more exact, we) were led to
this by the logical process of scientific evolution which often
leads to independent, almost simultaneous discoveries. Integrable,
or, more accurately, exactly solvable equations are essential to
theoretical and mathematical physics. One could say that they
constitute the "mathematical nucleus" of theoretical physics whose
goal is to describe real clas sical or quantum systems. For
example, the kinetic gas theory may be considered to be a theory of
a system which is trivially integrable: the system of classical
noninteracting particles. One of the main tasks of quantum
electrodynamics is the development of a theory of an integrable
perturbed quantum system, namely, noninteracting electromagnetic
and electron-positron fields."
1 2 V. E. Zakharov and S. Wabnitz 1 L. D. Landau Institute for
Theoretical Physics, 2 Kosygin Str., 117334 Moscow, Russia 2
Laboratoire de Physique, University of Bourgogne, 9 avenue A.
Savary, 21078 Dijon, France After about a quarter of a century
since the first theoretical predictions of op tical solitons, the
industrial application of the optical soliton concept is near to
reality in the booming field of modern telecommunications, where
the de mand for high-speed data transmission and routing is of
ever-growing. This book contains a set of lectures that were
presented at a Les Houches school on optical solitons in September
1998. The school was successful in gathering among the lecturers
most of the well-recognized world leaders in the field of optical
solitons. A variety of different aspects of research into optical
solitons was exposed in the lectures, ranging from the mathematical
fundations of integrability theory to the rapidly evolving
technological advances of fiber soliton-based telecommu nication
systems. The overall impression that the participants and the
students received from the school is that this field of research is
an excellent example of the rapid transfer that occurs nowadays
from basic science to the technological implementations of the
first principles. The subjects that were covered by the lectures
can be broadly grouped into four main categories: optical soliton
the ory, fiber soliton telecommunications, optical soliton
generation methods, and all-optical information processing via
spatial solitons."
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