非線性孤立子和混沌

內(nèi)容概要

This revised and updated second edition.of a, highly successful book is the only text at this level to embrace a universai approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. .    A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Examples of these are coherent entities like nonlinear waves and solitons, as well as the incoherent structures associated with chaos. The first part of the book is a self-contained introduction to general topics associated with nonlinear graduate physics, and would be accessible to final-year undergraduates and beginning graduate students. The remainder of the book, for example the treatment of cylindrical solitons, is more advanced and will have a wide appeal to specialists in a number of branches of physics. Each chapter concludes with a set of problems. ..    This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will. be of value to final-year undergraduates and beginning graduate students studying fluid dynamics, plasma physics or applied mathematics.

書籍目錄

Foreword to the first edition . Foreword to the second edition 1 Introduction   1.1 Occurrence of nonlinear waves and instabilities in Nature     1.1.1 Nonlinear phenomena in our everyday experience     1.1.2 Nonlinear phenomena in the laboratory   1.2 Universal wave equations     1.2.1 The Korteweg-de Vries and Kadomtsev-Petviashvili equations and a first look at solitons     1.2.2 The nonlinear Schr6dingcr equation     1.2.3 Nonlinear optics   1.3 What is a plasma?   1.4 Wave modes on a water surface     1.4.1 Mathematicaltheory     1.4.2 Comments   1.5 Linear stability analysis and its limitations   1.6 Nonlinear structures     1.6.1 Coherent structures and pattern formation   1.7 Contents of Chapters 2-11 2 Linear waves and instabilities in infinite media   2.1 Introduction   2.2 Plasma waves  2.3 CMM diagrams  2.4 Instabilities  2.5 The Vlasov equations  2.6 Weak instabilites  Exercises3 Convective and non-convective instabilities;guoup velcoity in unstable media  3.1 Introdction  3.2 Kinematics of unstable wavepackets  ……4 A first look at surface waves and instabilities5 Model equations for small amplitued waves and solitons;weakly nonlinear theory6 Exact methods for fully nonlinear waves and solitons7 Cartesian solitons in ond the two space dimensions8 Evolution and stability of initially one-dimensional waves and solitons9 Cylindrical and spherical solitons in palsmas and other media10 Soliton metamorphosis11 Non-coerent phenomenaAppendicesReferencesAuthor indexSubject index

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