Nonlinear Waves & Hamiltonian Systems : From One to Many Degrees of Freedom, from Discrete to Continuum

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Nonlinear Waves & Hamiltonian Systems : From One to Many Degrees of Freedom, from Discrete to Continuum

Carretero-González, Ricardo/ Frantzeskakis, Dimitrios J./ Kevrekidis, Panayotis G.

ウェブストア価格 ¥40,144（本体¥36,495）
Oxford University Press（2024/11発売）
外貨定価 UK£ 132.00
ポイント 364pt

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製本 Hardcover:ハードカバー版／ページ数 560 p.
言語 ENG
商品コード 9780192843234
DDC分類 531.1133

Full Description

Nonlinear waves are of significant scientific interest across many diverse contexts, ranging from mathematics and physics to engineering, biosciences, chemistry, and finance. The study of nonlinear waves is relevant to Bose-Einstein condensates, the interaction of electromagnetic waves with matter, optical fibers and waveguides, acoustics, water waves, atmospheric and planetary scales, and even galaxy formation.

The aim of this book is to provide a self-contained introduction to the continuously developing field of nonlinear waves, that offers the background, the basic ideas, and mathematical, as well as computational methods, while also presenting an overview of associated physical applications.

Originated from the authors' own research activity in the field for almost three decades and shaped over many years of teaching on relevant courses, the primary purpose of this book is to serve as a textbook. However, the selection and exposition of the material will be useful to anyone who is curious to explore the fascinating world of nonlinear waves.

PART I - INTRODUCTION AND MOTIVATION OF MODELS 1: Introduction and Motivation 2: Linear Dispersive Wave Equations 3: Nonlinear Dispersive Wave Equations PART II - KORTEWEG-DE VRIES (KDV) EQUATION 4: The Korteweg-de Vries (KdV) Equation 5: From Boussinesq to KdV - Boussinesq Solitons as KdV Solitons 6: Traveling Wave Reduction, Elliptic Functions, and Connections to KdV 7: Burgers and KdV-Burgers (KdVB) Equations - Regularized ShockWaves 8: A Final Touch From KdV: Invariances and Self-Similar Solutions 9: Spectral Methods 10: Bäcklund Transformation for the KdV 11: Inverse Scattering Transform I - the KdV equation* 12: Direct Perturbation Theory for Solitons* 13: The Kadomtsev-Petviashvili Equation* PART III - KLEIN-GORDON, SINE-GORDON, AND PHI-4 MODELS 14: Another Class of Models: Nonlinear Klein-Gordon Equations 15: Additional Tools/Results for Klein-Gordon Equations 16: Klein-Gordon to NLS Connection - Breathers as NLS Solitons 17: Interlude: Numerical Considerations for Nonlinear Wave Equations PART IV - THE NONLINEAR SCHRÖDINGER EQUATIONS 18: The Nonlinear Schrödinger (NLS) Equation 19: NLS to KdV Connection - Dark Solitons as KdV Solitons 20: Actions, Symmetries, Conservation Laws, Noether's Theorem, and all that 21: Applications of Conservation Laws - Adiabatic Perturbation Method 22: Numerical Techniques for NLS 23: Inverse Scattering Transform II - the NLS Equation* 24: The Gross-Pitaevskii (GP) Equation 25: Variational Approximation for the NLS and GP Equations 26: Stability Analysis in 1D 27: Multi-Component Systems 28: Transverse Instability of Solitons Stripes - Perturbative Approach 29: Transverse Instability of Dark Stripes - Adiabatic Invariant Approach 30: Vortices in the 2D Defocusing NLS PART V - DISCRETE MODELS 31: The Discrete Klein-Gordon model 32: Discrete Models of the Nonlinear Schrödinger Type 33: From Toda to FPUT and Beyond