Solitary Waves in Dispersive Complex Media. Theory, Simulation, Applications

Группа	Научная литература
Область науки	Естественные науки
Название на русском языке	Solitary Waves in Dispersive Complex Media. Theory, Simulation, Applications
Авторы на русском языке	Belashov V.Yu., Vladimirov S.V.
Издательство на русском языке	Berlin Heidelberg, 2005. - 303 p.

Abstract

This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics – to theoretical, analytical and numerical study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear wave packets described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrödinger (NLS) and derivative NLS (DNLS) classes of equations. Special attention is paid to generalizations (relevant to various complex physical media) of these equations, accounting for higher-order dispersion corrections, influence of dissipation, instabilities, and stochastic fluctuations of the wave fields.

This book is a coordinated approach to the theory, simulations, and applications of nonlinear one-, two-, and three-dimensional solitary wave solutions. Overall, the content of the book is a systematic account of results not only already known in the literature, but also those of new original studies related to the theory of models allowing soliton solutions, and analyses of stability and asymptotics of these solutions. Significant consideration is given to numerical methods and results of numerical simulations of the structure and dynamics of solitons and nonlinear wave packets. Together with deep insights into the theory, applications to various branches of modern physics are considered, especially to plasma physics (such as space plasmas including ionospheric and magnetospheric processes), hydrodynamics, and atmosphere dynamics.

We also note that content of this book is a result of generalization of the author’s teaching experience in the development of and reading the courses on the theory and numerical modeling of the nonlinear wave dynamics for students at graduate and post-graduate levels. This strongly influenced the structure of the book; we also hope that the methodic of selection and presentation of the content will allow to use this publication as a reference book not only by students but also by scientists in various fields of modern physics. We thus address this publication to researchers working in the theory and numerical simulations of dispersive complex media in such fields as hydrodynamics, plasma physics, and aero-dynamics. As a reference book, we expect the monograph to be useful for graduate and post-graduate students majoring in physics and mathematics as well as for scientists interested in solitons and nonlinear waves in other dispersive complex systems.

This work is partially supported by the Russian Foundation for Fundamental Research (Grant № 01-02-16116) and the Australian Research Council.

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