Nonlinear Waves & Hamiltonian Systems
From One To Many Degrees of Freedom, From Discrete To Continuum
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Product details:
- Edition number 1
- Publisher OUP Oxford
- Date of Publication 5 November 2024
- ISBN 9780192843241
- Binding Paperback
- No. of pages560 pages
- Size 245x190x27 mm
- Weight 1160 g
- Language English 535
Categories
Short description:
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.
MoreLong 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.
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 primarypurpose 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.
Table of Contents:
PART I - INTRODUCTION AND MOTIVATION OF MODELS
Introduction and Motivation
Linear Dispersive Wave Equations
Nonlinear Dispersive Wave Equations
PART II - KORTEWEG-DE VRIES (KDV) EQUATION
The Korteweg-de Vries (KdV) Equation
From Boussinesq to KdV - Boussinesq Solitons as KdV Solitons
Traveling Wave Reduction, Elliptic Functions, and Connections to KdV
Burgers and KdV-Burgers (KdVB) Equations - Regularized ShockWaves
A Final Touch From KdV: Invariances and Self-Similar Solutions
Spectral Methods
Bäcklund Transformation for the KdV
Inverse Scattering Transform I - the KdV equation*
Direct Perturbation Theory for Solitons*
The Kadomtsev-Petviashvili Equation*
PART III - KLEIN-GORDON, SINE-GORDON, AND PHI-4 MODELS
Another Class of Models: Nonlinear Klein-Gordon Equations
Additional Tools/Results for Klein-Gordon Equations
Klein-Gordon to NLS Connection - Breathers as NLS Solitons
Interlude: Numerical Considerations for Nonlinear Wave Equations
PART IV - THE NONLINEAR SCHRÖDINGER EQUATIONS
The Nonlinear Schrödinger (NLS) Equation
NLS to KdV Connection - Dark Solitons as KdV Solitons
Actions, Symmetries, Conservation Laws, Noether's Theorem, and all that
Applications of Conservation Laws - Adiabatic Perturbation Method
Numerical Techniques for NLS
Inverse Scattering Transform II - the NLS Equation*
The Gross-Pitaevskii (GP) Equation
Variational Approximation for the NLS and GP Equations
Stability Analysis in 1D
Multi-Component Systems
Transverse Instability of Solitons Stripes - Perturbative Approach
Transverse Instability of Dark Stripes - Adiabatic Invariant Approach
Vortices in the 2D Defocusing NLS
PART V - DISCRETE MODELS
The Discrete Klein-Gordon model
Discrete Models of the Nonlinear Schrödinger Type
From Toda to FPUT and Beyond
