3 edition of **Nonlinear Wave Equations** found in the catalog.

- 119 Want to read
- 3 Currently reading

Published
**August 2000** by American Mathematical Society .

Written in English

- Differential equations,
- Non-linear science,
- Theoretical methods,
- Mathematics,
- Science,
- Science/Mathematics,
- Waves & Wave Mechanics,
- Linear Programming,
- Congresses,
- Nonlinear wave equations

**Edition Notes**

Contributions | Walter A. Strauss (Editor), Yan Guo (Editor) |

The Physical Object | |
---|---|

Format | Paperback |

Number of Pages | 201 |

ID Numbers | |

Open Library | OL11419905M |

ISBN 10 | 0821820710 |

ISBN 10 | 9780821820711 |

Find many great new & used options and get the best deals for De Gruyter Expositions in Mathematics: Nonlinear Wave Equations Perturbed by the Viscous Term 31 by Peter Petrovich Mosolov and V. P. Maslov (, Hardcover) at the best online prices at eBay! Free shipping for many products! This method of solution of () is easily extended to nonlinear equations of the form ut +aux =f(t,x,u). () See Exercises , , and for more on nonlinear equations of this form. SystemsofHyperbolicEquations We now examine systems of hyperbolic equations with constant coefﬁcients in one space Size: 1MB.

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This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space Cited by: 7.

This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space.

Book Description. 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 Nonlinear Wave Equations book methods.

About this book Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared indue to the increased use of nonlinear waves.

It covers the behavior of waves Nonlinear Wave Equations book two Nonlinear Wave Equations book, with the first part addressing hyperbolic waves and the second addressing dispersive waves.

This book, based Nonlinear Wave Equations book lectures presented by the author at George Mason University in Januaryseeks 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 by: @article{osti_, title = {Solitons and nonlinear wave equations}, author = {Dodd, Roger K and Eilbeck, J Chris and Gibbon, John D and Morris, Hedley C}, abstractNote = {A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory.

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Containing key bibliographic citations, Nonlinear Wave Nonlinear Wave Equations book is an excellent reference for mathematical analysts and industrial and applied mathematicians; electrical and electronics, aerospace, mechanical, control, systems, and computer engineers; and physicists; as well as an invaluable text for graduate-level students in these.

It follows that p also satisﬁes the wave equation. The nonlinear equations of gas dynamics will be discussed in Chapter 4. We have assumed that the waves are even in x ct. To ﬁnd the most general form of the wave we also have to include terms of the form sin(k(x ct)).

In File Size: 1MB. equation, the semilinear wave equation, Nonlinear Wave Equations book Korteweg-de Vries equation, and the wave maps equation. These four equations are of course only a very small sample of the nonlinear dispersive equations studied in the literature, but they are reasonably representative in that they showcase many of the techniques used for more general.

The Nonlinear Wave Equations book of nonlinear wave equations in the absence of shocks began in the s. This book surveys the fundamental qualitative properties of the. 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. This book, based on lectures presented by the author at George Mason University in Januaryseeks to present the sharpest Nonlinear Wave Equations book to date in this author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks/5(1).

This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in Brand: Springer Berlin Heidelberg.

Nonlinear Wave Equations - CRC Press Book 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 st. This book discusses as well nonlinear hyperbolic equations in further contributions, featuring stability properties of periodic and almost periodic solutions.

The reader is also introduced to the stability problem of the equilibrium of a chemical network. The final chapter deals with suitable spaces for studying functional equations.

This book, based on lectures presented by the author at George Mason University in Januaryseeks 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.

In book: Harmonic Analysis and Wave Equations, pp Cite this publication This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of. The ordinary wave equation is linear, and always shows fairly simple behavior.

The sine-Gordon equation is nonlinear, but is still special in having solitons. Nonlinear Evolution Equations and Gardner reveal that a large number of equations governing nonlinear wave motion can be put in a Hamiltonian formalism. Many of these equations turn out to be completely integrable.

This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws. Dynamics of Nonlinear Wave Equations, One Chapter of the book: Harmonic analysis and wave equations Book September with Reads How we measure 'reads'.

Nonlinear optics is the discipline in which the electric polarization density of the medium is studied as a nonlinear function of the electromagnetic field of the light. This text is an introduction to the phenomena encountered in nonlinear optics.

This culminates in a presentation of the proof of the soliton resolution conjecture for the three-dimensional radial focusing energy critical wave equation. It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations.

A co-publication of the AMS and CBMS. 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/5(2).

Book of Abstracts The Eleventh IMACS International Conference On Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory Athens, Georgia April 17—19, Sponsored by The International Association for Mathematics and Computers in Simulation (IMACS) The Computer Science Department, University of GeorgiaFile Size: 1MB.

Walter Strauss' Partial Differential Equations: An Introduction is pretty standard as far as undergraduate texts go. It seems pretty good to me, although it contains many errors, especially in the first edition.

(Errata) The presentation style is. Solitary Wave Nonlinear Wave Equation High Order Equation Linear Wave Equation Galilean Invariance These keywords were added by machine and not by the authors. This process is experimental and the keywords may be Cited by: As an example of wave propagation in nonlinear optical media, the optical Kerr effect is analysed for infinite plane continuous waves.

instead of by means of a perturbation series as above, the Maxwell equations and the wave equation in Butcher and Cotter's book, which hence should be taken with some care if one wish to build a strict. AbstractIn this paper, we consider the initial boundary value problem for a class of fourth-order wave equations with strong damping term, nonlinear weak damping term, strain term and nonlinear source term in polynomial form.

First, the local solution is obtained by using fix point theory. Then, by constructing the potential well structure frame, we get the global existence, Cited by: 4.

Chapter 2 Wave-Equation Description of Nonlinear Optical Interactions. The Wave Equation for Nonlinear Optical Media. We have seen in the last chapter how nonlinearity in the response of a material system to an intense laser field can cause the polarization of the medium to develop new frequency components not present in the incident radiation field.

This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates.

In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation. An algorithm for the solution of general isotropic nonlinear wave equations is presented.

The algorithm is based on a symmetric factorization of the linear part of the wave operator, followed by its exact integration through an integrating factor in spectral by: () nonlinear wave equations and reaction–diffusion equations with several nonlinear source terms of different signs at high energy level.

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Hereman, Colorado School of Mines, Golden, CO and Barbara Prinari, University of Colorado, Colorado Springs, Colorado Springs, CO, Editors.

In the study of the Cauchy problem for nonlinear wave equations with small initial data, the case where the nonlinearity has the critical power is of special interest. In this case, depending on the structure of the nonlinearity, one may observe global existence and finite time blow-up of solutions.

Nonlinear acoustics (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes.

Large amplitudes require using full systems of governing equations of fluid dynamics (for sound waves in liquids and gases) and elasticity (for sound waves in solids). These equations are generally nonlinear, and their traditional linearization is no longer possible.

Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem 4/5(1).

The investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth of interest in nonlinear acoustic phenomena.

In this book, the authors consider models of different "acoustic" media as well as. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of by: Local and Global Analysis of Nonlinear Dispersive and Wave Equations book.

Read reviews from world’s largest community for readers. Among nonlinear PDEs, 5/5(3). This book, based on pdf presented by the author at George Mason University in Januaryseeks to present the sharpest results to date in this author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks.5/5(1).

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The readers will witness the major development with the introduction of modern harmonic analysis and related techniques. Sample Chapter(s) Preface Lectures on Nonlinear Wave Equations.

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