TY  - BOOK
AU  - Tobisch,Elena
TI  - New approaches to nonlinear waves
T2  - Lecture notes in physics,
SN  - 9783319206905
AV  - QA927 
U1  - 530.12/4 23
PY  - 2015///]
CY  - Cham
PB  - Springer
KW  - Nonlinear waves
KW  - Ondes non linéaires
KW  - Classical mechanics
KW  - bicssc
KW  - Statistical physics
KW  - Geophysics
KW  - Mathematical physics
KW  - Science
KW  - Mechanics
KW  - General
KW  - bisacsh
KW  - Physics
KW  - Mathematical Physics
KW  - fast
KW  - biofysica
KW  - biophysics
KW  - fysica
KW  - physics
KW  - mathematische natuurkunde
KW  - mathematical physics
KW  - geofysica
KW  - geophysics
KW  - Physics (General)
KW  - Fysica (algemeen)
N1  - Includes bibliographical references and index; Introduction (E. Tobisch) -- Brief historical overview -- Main notions -- Resonant interactions -- Modulation instability -- Frameworks -- Reality check -- References -- The effective equation method (Sergei Kuksin and Alberto Maiocchi) -- Introduction -- How to construct the effective equation -- Structure of resonances -- CHM: resonance clustering -- Concluding remarks -- References -- On the discovery of the steady-state resonant water waves (Shijun Liao, Dali Xu and Zeng Liu) -- Introduction -- Basic ideas of homotopy analysis method -- Steady-state resonant waves in constant-depth water -- Experimental observation -- Concluding remarks -- References -- Modulational instability in equations of KdV type (Jared C. Bronski, Vera Mikyoung Hur and Mathew A. Johnson) -- Introduction -- Periodic traveling waves of generalized KdV equations -- Formal asymptotics and Whitham's modulation theory -- Rigorous theory of modulational instability -- Applications -- Concluding remarks -- References -- Modulational instability and rogue waves in shallow water models (R. Grimshaw, K. W. Chow and H. N. Chan) -- Introduction -- Korteweg-de Vries equations --  Boussinesq model -- Hirota-Satsuma model -- Discussion -- References -- Hamiltonian framework for short optical pulses (Shalva Amiranashvili) -- Introduction --  Poisson brackets --  Pulses in optical fibers --  Hamiltonian description of pulses --  Concluding remarks -- References -- Modeling water waves beyond perturbations (Didier Clamond and Denys Dutykh) -- Introduction -- Preliminaries -- Variational formulations -- Examples -- Discussion -- References -- Quantitative Analysis of Nonlinear Water-Waves: a Perspective of an Experimentalist (Lev Shemer) -- Introduction -- The experimental facilities -- The Nonlinear Schrödinger Equation -- The Modified Nonlinear Schrödinger (Dysthe) Equation -- The Spatial Zakharov Equation --  Statistics of nonlinear unidirectional water waves -- Discussion and Conclusions -- References
N2  - The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems; The introductory chapter provides a general overview, thematically linking the objects described in the book; Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3); In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5); The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system; The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments; All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g; Equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima, KdV-type, Klein-Gordon, NLS-type, Serre, Shamel, Whitham and Zakharov; This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects; The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-319-20690-5
ER  -