Introduction To The Mathematical Physics Of Nonlinear Waves

Author : Minoru Fujimoto
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1627052771
Total Pages : 217 pages
Book Rating : 4.71/5 ( download)

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Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by Minoru Fujimoto and published by Morgan & Claypool Publishers. This book was released on 2014-03-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment

Author : M Fujimoto
Publisher : Myprint
ISBN 13 : 9781681747941
Total Pages : 158 pages
Book Rating : 4.44/5 ( download)

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Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by M Fujimoto and published by Myprint. This book was released on 2014-02-28 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Minoru Fujimoto
Publisher :
ISBN 13 : 9780750337588
Total Pages : pages
Book Rating : 4.83/5 ( download)

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Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by Minoru Fujimoto and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for students at upper-undergraduate and graduate levels, it is suitable for advanced physics courses on nonlinear physics. The book covers the fundamental properties of nonlinear waves, dealing with both theory and experiment. The aim is to emphasize established tools and introduce new methods underpinning important new developments in this field, especially as applied to solid-state materials. The updated edition has been extended to emphasize the importance of thermodynamics in a description of modulated crystals and contains new chapters on superconductivity that can be interpreted by the soliton mechanism. It is also updated to include new end-of-chapter problems.

Author : Peter R. Popivanov
Publisher : World Scientific
ISBN 13 : 9814322121
Total Pages : 179 pages
Book Rating : 4.26/5 ( download)

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Download or read book Nonlinear Waves written by Peter R. Popivanov and published by World Scientific. This book was released on 2011 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Big Nate is the star goalie of his school's soccer team, and he is tasked with defending his goal and saving the day against Jefferson Middle School, their archrival.

Author : FUJIMOTO
Publisher :
ISBN 13 : 9780750337601
Total Pages : pages
Book Rating : 4.05/5 ( download)

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Download or read book Introduction Mathematical Physics Nonl written by FUJIMOTO and published by . This book was released on 2021-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Elena Tobisch
Publisher : Springer
ISBN 13 : 3319206907
Total Pages : 298 pages
Book Rating : 4.05/5 ( download)

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Download or read book New Approaches to Nonlinear Waves written by Elena Tobisch and published by Springer. This book was released on 2015-08-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Angela Slavova
Publisher : World Scientific Publishing
ISBN 13 : 9813271620
Total Pages : 208 pages
Book Rating : 4.23/5 ( download)

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Download or read book Nonlinear Waves: A Geometrical Approach written by Angela Slavova and published by World Scientific Publishing. This book was released on 2018-11-16 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.

Author : Mitsuhiro Tanaka
Publisher : Springer Nature
ISBN 13 : 303102611X
Total Pages : 237 pages
Book Rating : 4.19/5 ( download)

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Download or read book Physics of Nonlinear Waves written by Mitsuhiro Tanaka and published by Springer Nature. This book was released on 2022-05-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book about nonlinear waves. It focuses on two properties that various different wave phenomena have in common, the "nonlinearity" and "dispersion", and explains them in a style that is easy to understand for first-time students. Both of these properties have important effects on wave phenomena. Nonlinearity, for example, makes the wave lean forward and leads to wave breaking, or enables waves with different wavenumber and frequency to interact with each other and exchange their energies. Dispersion, for example, sorts irregular waves containing various wavelengths into gentler wavetrains with almost uniform wavelengths as they propagate, or cause a difference between the propagation speeds of the wave waveform and the wave energy. Many phenomena are introduced and explained using water waves as an example, but this is just a tool to make it easier to draw physical images. Most of the phenomena introduced in this book are common to all nonlinear and dispersive waves. This book focuses on understanding the physical aspects of wave phenomena, and requires very little mathematical knowledge. The necessary minimum knowledges about Fourier analysis, perturbation method, dimensional analysis, the governing equations of water waves, etc. are provided in the text and appendices, so even second- or third-year undergraduate students will be able to fully understand the contents of the book and enjoy the fan of nonlinear wave phenomena without relying on other books.

Author : Roger Knobel
Publisher : American Mathematical Soc.
ISBN 13 : 0821820397
Total Pages : 212 pages
Book Rating : 4.91/5 ( download)

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Download or read book An Introduction to the Mathematical Theory of Waves written by Roger Knobel and published by American Mathematical Soc.. This book was released on 2000 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow. The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as MathematicaR, MATLABR, or MapleR is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.

Author : Minoru Fujimoto
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1627052763
Total Pages : 156 pages
Book Rating : 4.64/5 ( download)

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Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by Minoru Fujimoto and published by Morgan & Claypool Publishers. This book was released on 2014-03-01 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment