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020 _a9783319206905
_9978-3-319-20690-5
024 7 _a10.1007/978-3-319-20690-5
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.1
_223
245 1 0 _aNew Approaches to Nonlinear Waves
_h[electronic resource] /
_cedited by Elena Tobisch.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXV, 298 p. 65 illus., 15 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v908
505 0 _aIntroduction (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.
520 _aThe 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.    .
650 0 _aStatistical physics.
650 1 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
650 2 4 _aClassical and Continuum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P2100X
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aGeophysics and Environmental Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P32000
650 2 4 _aStatistical Physics and Dynamical Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P19090
700 1 _aTobisch, Elena.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319206899
776 0 8 _iPrinted edition:
_z9783319206912
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v908
856 4 0 _uhttps://doi.org/10.1007/978-3-319-20690-5
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c12372
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