Nonlinear Waves Hamiltonian Systems
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Nonlinear Waves Hamiltonian Systems
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Author : Ricardo Carretero-González
language : en
Publisher: Oxford University Press
Release Date : 2025-01-28
Nonlinear Waves Hamiltonian Systems written by Ricardo Carretero-González and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-28 with Mathematics categories.
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.
Nonlinear Waves And Hamiltonian Systems
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Author : Ricardo Carretero-González
language : en
Publisher: Oxford University Press
Release Date : 2025-01-28
Nonlinear Waves And Hamiltonian Systems written by Ricardo Carretero-González and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-28 with Mathematics categories.
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.
Stability Of Nonlinear Waves In Hamiltonian Dynamial Systems
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Author : Anna Geyer
language : en
Publisher:
Release Date : 2025
Stability Of Nonlinear Waves In Hamiltonian Dynamial Systems written by Anna Geyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with categories.
This monograph offers a comprehensive and accessible treatment of both classical and modern approaches to the stability analysis of nonlinear waves in Hamiltonian systems. Starting with a review of stability of equilibrium points and periodic orbits in finite-dimensional systems, it advances to the infinite-dimensional setting, addressing orbital stability and linearization techniques for spatially decaying and spatially periodic solutions of nonlinear dispersive wave equations, such as the nonlinear Schrodinger, Korteweg-de Vries, and Camassa-Holm equations. The book rigorously develops foundational tools, such as the Vakhitov-Kolokolov slope criterion, the Grillakis-Shatah-Strauss approach, and the integrability methods, but it also introduces innovative adaptations of the stability analysis in problems where conventional methods fall short, including instability of peaked traveling waves and stability of solitary waves over nonzero backgrounds. Aimed at graduate students and researchers, this monograph consolidates decades of research and presents recent advancements in the field, making it an indispensable resource for those studying the stability of nonlinear waves in Hamiltonian systems.
Nonlinear Waves
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Author : Emmanuel Kengne
language : en
Publisher: Springer Nature
Release Date : 2023-02-23
Nonlinear Waves written by Emmanuel Kengne and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-23 with Science categories.
This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.
Dynamical Systems And Nonlinear Waves In Plasmas
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Author : Asit Saha
language : en
Publisher: CRC Press
Release Date : 2021-09-09
Dynamical Systems And Nonlinear Waves In Plasmas written by Asit Saha and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Science categories.
Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.
Nonlinear Waves And Weak Turbulence
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Author : Vladimir Evgenʹevich Zakharov
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Nonlinear Waves And Weak Turbulence written by Vladimir Evgenʹevich Zakharov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincare normal forms and the inverse scattering method.
Nonlinear Waves In Integrable And Non Integrable Systems
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Author : Jianke Yang
language : en
Publisher: SIAM
Release Date : 2010-12-02
Nonlinear Waves In Integrable And Non Integrable Systems written by Jianke Yang and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-02 with Science categories.
Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
Nonlinear Waves 3
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Author : Andrei V. Gaponov-Grekhov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Waves 3 written by Andrei V. Gaponov-Grekhov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet Scientists working in this field. Since 1989 the proceedings appear in English. They present a good cross section of nonlinear physics in the USSR. This third volume emerged from material presented at the 1989 School. It contains sections dealing with nonlinear problems in physics and astrophysics, quantum and solid state physics, dynamical chaos and self-organization.
New Approaches To Nonlinear Waves
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Author : Elena Tobisch
language : en
Publisher: Springer
Release Date : 2015-08-19
New Approaches To Nonlinear Waves written by Elena Tobisch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Science categories.
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.
Nonlinear Waves And Weak Turbulence
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Author : FITZMAURICE
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Waves And Weak Turbulence written by FITZMAURICE and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V. E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing developments in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which for the most part are concerned with the application of the theory in various fields. While the word "turbulence" is most often associated with f:l. uid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas: • The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence. • Statistical studies of fully developed turbulent systems. In hydrodynamics, work on the transition question dates back to the end of the last century with pioneering contributions by Osborne Reynolds and Lord Rayleigh.