Nonlinear Wave Equations Perturbed By Viscous Terms

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Nonlinear Wave Equations Perturbed by Viscous Terms

Author : Petr P. Mosolov
Publisher : Walter de Gruyter
ISBN 13 : 3110811901
Total Pages : 341 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Nonlinear Wave Equations Perturbed by Viscous Terms by : Petr P. Mosolov

Download or read book Nonlinear Wave Equations Perturbed by Viscous Terms written by Petr P. Mosolov and published by Walter de Gruyter. This book was released on 2011-07-20 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Nonlinear Waves in Fluids: Recent Advances and Modern Applications

Author : Roger Grimshaw
Publisher : Springer Science & Business Media
ISBN 13 : 3211380256
Total Pages : 202 pages
Book Rating : 4.2/5 (113 download)

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Book Synopsis Nonlinear Waves in Fluids: Recent Advances and Modern Applications by : Roger Grimshaw

Download or read book Nonlinear Waves in Fluids: Recent Advances and Modern Applications written by Roger Grimshaw and published by Springer Science & Business Media. This book was released on 2007-03-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.

Nonlinear Wave Equations

Author : Yan Guo
Publisher : American Mathematical Soc.
ISBN 13 : 0821820710
Total Pages : 216 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonlinear Wave Equations by : Yan Guo

Download or read book Nonlinear Wave Equations written by Yan Guo and published by American Mathematical Soc.. This book was released on 2000 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents original research papers and expository articles from the conference in honour of Walter A. Strauss's 60th birthday, held at Brown University in Providence, Rhode Island. The book offers a collection of original papers and expository articles mainly devoted to the study of nonlinear wave equations. The articles cover a wide range of topics, including scattering theory, dispersive waves, classical field theory, mathematical fluid dynamics, kinetic theory, stability theory, and variational methods. The book offers a cross-section of current trends and research directions in the study of nonlinear wave equations and related topics.

Nonlinear Wave Equations

Author : Walter A. Strauss
Publisher : American Mathematical Soc.
ISBN 13 : 0821807250
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonlinear Wave Equations by : Walter A. Strauss

Download or read book Nonlinear Wave Equations written by Walter A. Strauss and published by American Mathematical Soc.. This book was released on 1990-01-12 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Wave Equations

Author : Satyanad Kichenassamy
Publisher : CRC Press
ISBN 13 : 1000444724
Total Pages : 297 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Nonlinear Wave Equations by : Satyanad Kichenassamy

Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy and published by CRC Press. This book was released on 2021-05-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Nonlinear Random Waves

Author : Vladimir V. Konotop
Publisher : World Scientific
ISBN 13 : 9789810217259
Total Pages : 312 pages
Book Rating : 4.2/5 (172 download)

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Book Synopsis Nonlinear Random Waves by : Vladimir V. Konotop

Download or read book Nonlinear Random Waves written by Vladimir V. Konotop and published by World Scientific. This book was released on 1994 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Waves

Author : Lokenath Debnath
Publisher : Cambridge University Press
ISBN 13 : 0511868618
Total Pages : 372 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis Nonlinear Waves by : Lokenath Debnath

Download or read book Nonlinear Waves written by Lokenath Debnath and published by Cambridge University Press. This book was released on 2009-01-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Nonlinear Stability of Shock Waves for Viscous Conservation Laws

Author : Tai-Ping Liu
Publisher : American Mathematical Soc.
ISBN 13 : 0821823299
Total Pages : 117 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonlinear Stability of Shock Waves for Viscous Conservation Laws by : Tai-Ping Liu

Download or read book Nonlinear Stability of Shock Waves for Viscous Conservation Laws written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 1985 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we establish the nonlinear stability of shock waves for viscous conservation laws. It is shown that when the initial data is a perturbation of viscous shock waves, then the solution converges to viscous shock waves, properly translated, as time tends to infinity.

A Perturbation Method for Treating Some Nonlinear Wave Equations

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (113 download)

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Book Synopsis A Perturbation Method for Treating Some Nonlinear Wave Equations by :

Download or read book A Perturbation Method for Treating Some Nonlinear Wave Equations written by and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solitons and Nonlinear Wave Equations

Author : Roger K. Dodd
Publisher :
ISBN 13 :
Total Pages : 650 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Solitons and Nonlinear Wave Equations by : Roger K. Dodd

Download or read book Solitons and Nonlinear Wave Equations written by Roger K. Dodd and published by . This book was released on 1982 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Waves: A Geometrical Approach

Author : Angela Slavova
Publisher : World Scientific Publishing
ISBN 13 : 9813271620
Total Pages : 208 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Nonlinear Waves: A Geometrical Approach by : Angela Slavova

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.

Nonlinear Dispersive Wave Systems

Author : Lokenath Debnath
Publisher : World Scientific
ISBN 13 : 9814554960
Total Pages : 683 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Nonlinear Dispersive Wave Systems by : Lokenath Debnath

Download or read book Nonlinear Dispersive Wave Systems written by Lokenath Debnath and published by World Scientific. This book was released on 1992-09-09 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known researchers who have made significant contributions to nonlinear waves and nonlinear instability. This volume will be invaluable to applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and to anyone interested in nonlinear dynamics.

The Existence of Global Solutions of a Variational Nonlinear Wave Equation

Author : Tae-Wan Park
Publisher :
ISBN 13 :
Total Pages : 130 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis The Existence of Global Solutions of a Variational Nonlinear Wave Equation by : Tae-Wan Park

Download or read book The Existence of Global Solutions of a Variational Nonlinear Wave Equation written by Tae-Wan Park and published by . This book was released on 2005 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Waves and Optics

Author : Harish Parthasarathy
Publisher : CRC Press
ISBN 13 : 1000372278
Total Pages : 524 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Waves and Optics by : Harish Parthasarathy

Download or read book Waves and Optics written by Harish Parthasarathy and published by CRC Press. This book was released on 2021-02-07 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers all aspects of waves and optics ranging from one dimensional waves in a vibrating string, two dimensional waves in a vibrating membrane, both of which are transverse, three dimensional electromagnetic waves generated by radiating antennas and longitudinal sound/pressure waves in an air column. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

Analytical And Numerical Methods For Wave Propagation In Fluid Media

Author : Krzysztof Murawski
Publisher : World Scientific
ISBN 13 : 9814487562
Total Pages : 255 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Analytical And Numerical Methods For Wave Propagation In Fluid Media by : Krzysztof Murawski

Download or read book Analytical And Numerical Methods For Wave Propagation In Fluid Media written by Krzysztof Murawski and published by World Scientific. This book was released on 2002-11-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance.Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons.

Nonlinear Waves in Elastic Crystals

Author : Gérard A. Maugin
Publisher :
ISBN 13 : 9780198534846
Total Pages : 328 pages
Book Rating : 4.5/5 (348 download)

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Book Synopsis Nonlinear Waves in Elastic Crystals by : Gérard A. Maugin

Download or read book Nonlinear Waves in Elastic Crystals written by Gérard A. Maugin and published by . This book was released on 1999 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.

Asymptotic Perturbation Theory Of Waves

Author : Lev Ostrovsky
Publisher : World Scientific
ISBN 13 : 178326473X
Total Pages : 227 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Asymptotic Perturbation Theory Of Waves by : Lev Ostrovsky

Download or read book Asymptotic Perturbation Theory Of Waves written by Lev Ostrovsky and published by World Scientific. This book was released on 2014-09-23 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theoretical ideas are illustrated by many physical examples throughout the book.