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Dispersive Equations and Nonlinear Waves

2014-07-14 Mathematics
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Release : 2014-07-14
Genre : Mathematics
Kind : eBook
Book Rating : 368/5 ( reviews)

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Book Synopsis Dispersive Equations and Nonlinear Waves by : Herbert Koch

Download or read book Dispersive Equations and Nonlinear Waves written by Herbert Koch. This book was released on 2014-07-14. Available in PDF, EPUB and Kindle. Book excerpt: 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, 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. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.​

Nonlinear Waves in One-dimensional Dispersive Systems

1979 Language Arts & Disciplines
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Release : 1979
Genre : Language Arts & Disciplines
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Nonlinear Waves in One-dimensional Dispersive Systems by : P. L. Bhatnagar

Download or read book Nonlinear Waves in One-dimensional Dispersive Systems written by P. L. Bhatnagar. This book was released on 1979. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Dispersive Wave Systems

1992-09-09
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Release : 1992-09-09
Genre :
Kind : eBook
Book Rating : 960/5 ( reviews)

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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. This book was released on 1992-09-09. 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.

Introduction to Nonlinear Dispersive Equations

2009-02-21 Mathematics
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Release : 2009-02-21
Genre : Mathematics
Kind : eBook
Book Rating : 991/5 ( reviews)

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Book Synopsis Introduction to Nonlinear Dispersive Equations by : Felipe Linares

Download or read book Introduction to Nonlinear Dispersive Equations written by Felipe Linares. This book was released on 2009-02-21. Available in PDF, EPUB and Kindle. Book excerpt: 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 information is then used to treat local and global well-posedness for the semi-linear Schrodinger equations. The end of each chapter contains recent developments and open problems, as well as exercises.

Linear and Nonlinear Waves

2011-10-18 Science
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Release : 2011-10-18
Genre : Science
Kind : eBook
Book Rating : 202/5 ( reviews)

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Book Synopsis Linear and Nonlinear Waves by : G. B. Whitham

Download or read book Linear and Nonlinear Waves written by G. B. Whitham. This book was released on 2011-10-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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