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Author : Peter R. Popivanov,Angela Slavova
Publisher : Unknown
Page : 209 pages
File Size : 41,6 Mb
Release : 2019
Category : Electronic
ISBN : 9813271612
Author : Angela Slavova,Petar Radoev Popivanov
Publisher : World Scientific Publishing
Page : 208 pages
File Size : 50,6 Mb
Release : 2018-11-16
Category : Mathematics
ISBN : 9789813271623
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 : Robert Hermann
Publisher : Unknown
Page : 610 pages
File Size : 54,8 Mb
Release : 1979
Category : Mathematics
ISBN : 0915692295
Author : Peter R. Popivanov,Angela Slavova
Publisher : World Scientific
Page : 179 pages
File Size : 49,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814322126
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 : Elena Tobisch
Publisher : Springer
Page : 298 pages
File Size : 45,6 Mb
Release : 2015-08-19
Category : Science
ISBN : 9783319206905
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 : Marcelo Anile,P Pantano,G Russo,J Hunter
Publisher : CRC Press
Page : 268 pages
File Size : 40,5 Mb
Release : 2021-06-24
Category : Mathematics
ISBN : 9781000447583
Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Author : Vladimir Evgenʹevich Zakharov
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 53,8 Mb
Release : 1998
Category : Hamiltonian systems
ISBN : 0821841130
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.
Author : Eryk Infeld,George Rowlands
Publisher : Cambridge University Press
Page : 416 pages
File Size : 43,6 Mb
Release : 2000-07-13
Category : Mathematics
ISBN : 0521635578
The second edition of a highly successful book on nonlinear waves, solitons and chaos.
Author : Walter A. Strauss
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 52,9 Mb
Release : 1990-01-12
Category : Mathematics
ISBN : 9780821807255
The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
Author : Vladimir V. Konotop,Luis V zquez
Publisher : World Scientific
Page : 312 pages
File Size : 55,7 Mb
Release : 1994
Category : Science
ISBN : 9810217250
This book is mainly devoted to the dynamics of the one-dimensional nonlinear stochastic waves. It contains a description of the basic mathematical tools as well as the latest results in the following fields: exactly integrable nonlinear stochastic equations, dynamics of the nonlinear waves in random media, evolution of the random waves in nonlinear media and the basic concepts of the numerical simulations in nonlinear random wave dynamics. A brief outline of the localization phenomenon in the nonlinear medium is also given. The approach is interdisciplinary describing the general methods with application to specific examples. The results presented may be useful for those who work in the areas of solid state physics, hydrodynamics, nonlinear optics, plasma physics, mathematical models of micromolecules and biological structures, ?etc. Since many results are based on the inverse scattering technique, perturbation theory for solitons and the methods of the statistical radiophysics, the terminology of the respective fields is used.
Author : G. B. Whitham
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 43,5 Mb
Release : 2011-10-18
Category : Science
ISBN : 9781118031209
Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.
Author : A M Kamchatnov
Publisher : World Scientific
Page : 396 pages
File Size : 41,8 Mb
Release : 2000-09-05
Category : Science
ISBN : 9789814492430
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics. This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions. Contents:Introduction and Basic ConceptsNonlinear Wave Equations in PhysicsWhitham Theory of ModulationsComplete Integrability of Nonlinear Wave EquationsPeriodic SolutionsDissipationless Shock WaveNonlinear Theory of Modulational InstabilityAppendices:Some Formulas from the Theory of Elliptic FunctionsAlgebraic Resolvents of Fourth Degree PolynomialsSolutions to Exercises Readership: Advanced graduate students and young researchers in nonlinear wave theory. Keywords:Nonlinear Waves;Solitons;Integrable Equations;Inverse Scattering Transform;Periodic Solutions;Whitham Theory;Modulation;Hodograph Transform;Dissipationless Shock Waves;Modulational Instability
Author : Robert Hermann
Publisher : Unknown
Page : 524 pages
File Size : 54,8 Mb
Release : 1979
Category : Mathematics
ISBN : STANFORD:36105031558336
Author : Jianke Yang
Publisher : SIAM
Page : 453 pages
File Size : 50,7 Mb
Release : 2010-01-01
Category : Science
ISBN : 9780898719680
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.
Author : Robert Hermann
Publisher : Unknown
Page : 526 pages
File Size : 48,9 Mb
Release : 1979
Category : Mathematics
ISBN : 0915692279
