Last edited by Voodookree

Tuesday, August 4, 2020 | History

4 edition of **Nonlinear dispersive equations** found in the catalog.

Nonlinear dispersive equations

Jaime Angulo Pava

- 368 Want to read
- 27 Currently reading

Published
**2009**
by American Mathematical Society in Providence, R.I
.

Written in English

- Nonlinear waves,
- Wave equation -- Numerical solution,
- Stability

**Edition Notes**

Includes bibliographical references and index.

Statement | Jaime Angulo Pava. |

Series | Mathematical surveys and monographs -- v. 156 |

Classifications | |
---|---|

LC Classifications | QA927 .A54 2009 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL24060477M |

ISBN 10 | 9780821848975 |

LC Control Number | 2009022821 |

OCLC/WorldCa | 401714023 |

Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers Brand: Springer New York.

This chapter discusses the application of a synergetic approach to the problems of nonlinear dispersive wave propagation and interaction. This book will prove useful to applied mathematicians, physicists, and engineers. Show less. Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers. of nonlinear and dispersive eﬀects in the medium. An interesting feature of solitons is that in spite of the fact that they are nonlinear phenomena, they behave “linearly” when they interact! We actually have an explicit form of solitons to a (generalized) KdV equation: u c,k(x,t) = Φ c,k(x −ct), for c > 0 where Φ c,k = c(k +2)/2sech2 File Size: KB.

The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger Brand: Birkhäuser Basel. Nonlinear Dispersive Equations: Professor Terence Tao: Books - Skip to main content. Try Prime EN Hello, Sign in Account & Lists Sign in Account & Lists Returns & Orders Try Prime Cart. Books. Go Search Hello Select your address 5/5(2).

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The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises.

Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students Cited by: This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution by: This collection of new and original papers on mathematical aspects of nonlinear dispersive equations includes both expository and technical papers that reflect a number of recent advances in the field.

The expository papers describe the state of the art and research directions.1/5(1). The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises.

Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers. Among nonlinear PDEs, dispersive and wave equations form an important class of equations.

These include the nonlinear Schrödinger 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 for such equations.

The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way.

The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev. Nonlinear Dispersive Equations: Local and Global Analysis, Issue American Mathematical Soc. 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.4/5(1).

The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems.

The research papers collected here include new results on the focusing nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as.

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 equations in a comparatively simple setting. Nonlinear Dispersive Equations: Local and Global Analysis Terence Tao Publication Year: ISBN ISBN CBMS Regional Conference Series in Mathematics, vol.

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 Price: $ The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way.

The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev cturer: Springer.

Nonlinear dispersive equations: local and global analysis. Terence Tao. CBMS regional conference series in mathematics, July Softcover, pages. ISBNISBN 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 5/5(3). The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation.

The energy-critical nonlinear Schrödinger equation. This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations.

Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way.

The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schrodinger equation to describe properties enjoyed by general dispersive equations.

This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations.

Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear SchrÃdinger 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 for such by: 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 in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves.See, for example, the books[5, 10] for the use of similar technique in the context of non-linear Schrödinger equation.

Technically, we divided the proof into two cases: 1 ≤ p.