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

ISBN-13: 9783642062407 / Angielski / Miękka / 2010 / 294 str.

Vasily Y. Belashov; Sergey V. Vladimirov

Opis

This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics theoretical, analytical andnumerical, studyofthestructureanddynamicsofone-dimensionalaswell as two- and three-dimensional solitons and nonlinear wave packets described by the Korteweg de Vries (KdV), Kadomtsev Petviashvili (KP), nonlinear Schr] odinger (NLS) and derivative nonlinear Schr] odinger (DNLS) classes of equations. Special attention is paid to generalizations (relevant to various complex physical media) of these equations, accounting for higher-order d- persion corrections, in?uence of dissipation, instabilities, and stochastic ?- tuations of the wave ?elds. We present here a coordinated approach to the theory, simulations, and applications of the nonlinear one-, two-, and three-dimensional solitary wave solutions. Overall, the content of the book is a systematic account of results notonlyalreadyknownintheliterature, butalsothoseofneworiginalstudies related to the theory of models allowing soliton solutions, and analyses of the stability and asymptotics of these solutions. We give signi?cant consideration 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. Presently, thetheoryofone-dimensionalnonlinearequationsoftheclasses consideredbytheauthorsiswelldeveloped, andtheprogressinstudiesofthe structure and evolution of one-dimensional solitons and wave packets is ob- ous. This progress was especially fast after the discovery of hidden algebraic symmetries of the KdV, NLS, and other (integrable by the inverse scatt- ing transform (IST) method) classes of one-dimensional evolution equations."

Recenzje

From the reviews:

"The book is devoted to one of the most interesting and rapidly developing areas of modern non-linear physics and mathematics ... . The book addresses researchers working in the theory and numerical simulations of dispersive complex media in such fields as hydrodynamics, plasma physics, and aerodynamics. It will also be useful as a reference work for graduate students in physics and mathematics." (Gai Bieng Zheng, Zentralblatt MATH, Vol. 1087, 2006)

"This book is concerned with the theoretical and numerical study of solitons and nonlinear wave packets ... . The authors present a unified approach to the theory, numerical approximation and applications of solitary wave solutions. Since it collects together many and diverse results in one of the most interesting and rapidly growing areas of modern nonlinear physics ... this monograph will prove very useful to researchers working in hydrodynamics, plasma physics, aerodynamics and in applied mathematics." (Mihai Maris, Mathematical Reviews, Issue 2007 a)

Spis treści

KdV-Class Solitons.- Generalized KdV Equations. NLS and DNLS Equations.- Classic Two- and Three-Dimensional KP Models and Their Applications.- Generalized Two- and Three-Dimensional Models and Their Applications.- Appendices.

Blurb

This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics - the theoretical, analytical and advanced numerical, study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves 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. The book addresses researchers working in the theory and numerical simulations of dispersive complex media in such fields as hydrodynamics, plasma physics, and aerodynamics. It will also be useful as a reference work for graduate students in physics and mathematics.