Nonlinear waves & Hamiltonian systems

• Verfasst von: Carretero-González, Ricardo [VerfasserIn]
• Verfasst von: Frantzeskakis, Dimitri J. [VerfasserIn]
• Verfasst von: Kevrekidis, Panayotis G. [VerfasserIn]
• Titel: Nonlinear waves & Hamiltonian systems
• Titelzusatz: from one to many degrees of freedom, from discrete to continuum
• Verf.angabe: R. Carretero-González (San Diego State University), Dimitrios Frantzeskakis (National and Kapodistrian University of Athens), P.G. Kevrekidis (University of Massachusetts, Amherst MA)
• Verlagsort: Oxford
• Verlag: Oxford University Press
• E-Jahr: 2024
• Jahr: [2024]
• Umfang: xx, 538 Seiten
• Illustrationen: Illustrationen, Diagramme
• Fussnoten: Literaturverzeichnis: Seite 524-534
• ISBN: 978-0-19-284323-4
• ISBN: 978-0-19-284324-1
• Sprache: eng
• RVK-Notation: UK 1200
• K10plus-PPN: 1909065749

Abstract

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.

Abstract

Cover -- Title page -- Copyright page -- Preface -- Acknowledgments -- Contents -- PART I INTRODUCTION AND MOTIVATION OF MODELS -- 1 Introduction and Motivation -- 1.1 Few degrees of freedom -- A linear example: Hooke's law -- A nonlinear example: the pendulum -- 1.2 Many degrees of freedom -- 1.3 A nonlinear variant: the FPUT lattice -- Exercises -- 2 Linear Dispersive Wave Equations -- 2.1 Dispersion relations and relevant notions -- 2.2 Examples of linear dispersive wave equations -- The transport (unidirectional wave) equation -- The (bidirectional) wave equation -- The linear Schrödinger equation -- 2.3 Wavepackets and group velocity -- 2.4 Dissipation, instability, and diffusion -- Exercises -- 3 Nonlinear Dispersive Wave Equations -- 3.1 Dispersion relations, linear and nonlinear equations -- 3.2 Unidirectional propagation: KdV, KP, and NLS -- The Korteweg-de Vries (KdV) equation -- Other versions of the KdV model -- The Kadomtsev-Petviashvili (KP) equation -- The nonlinear Schrödinger equation -- 3.3 Bidirectional propagation: KG and Boussinesq -- The Klein-Gordon equation -- The Boussinesq equation -- Exercises -- PART II KORTEWEG-DE VRIES (KDV) EQUATION -- 4 The Korteweg-de Vries (KdV) Equation -- 4.1 Obtaining KdV as a limit of FPUT -- 4.2 Obtaining KdV for shallow water waves -- 4.3 The effects of dispersion and nonlinearity -- The effect of dispersion - linearized KdV equation -- The effect of nonlinearity - Hopf equation, method of characteristics and shock waves -- 4.4 Putting it all together: the Zabusky-Kruskal numerical experiments -- 4.5 A cute twist: conservation laws -- Exercises -- 5 From Boussinesq to KdV - Boussinesq Solitons as KdV Solitons -- 5.1 Boussinesq to a single KdV (right-going waves) -- 5.2 Boussinesq to a KdV pair (right- and left-going waves) -- 5.3 Connecting the Boussinesq soliton with the KdV soliton.