Dispersive Equations and Nonlinear Waves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dispersive Equations and Nonlinear Waves write by Herbert Koch. This book was released on 2014-07-14. Dispersive Equations and Nonlinear Waves available in PDF, EPUB and Kindle. 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
Nonlinear Waves in One-dimensional Dispersive Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Waves in One-dimensional Dispersive Systems write by P. L. Bhatnagar. This book was released on 1979. Nonlinear Waves in One-dimensional Dispersive Systems available in PDF, EPUB and Kindle.
Nonlinear Dispersive Wave Systems
Nonlinear Dispersive Wave Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Dispersive Wave Systems write by Lokenath Debnath. This book was released on 1992-09-09. Nonlinear Dispersive Wave Systems available in PDF, EPUB and Kindle. 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.
Linear and Nonlinear Waves
Linear and Nonlinear Waves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Nonlinear Waves write by G. B. Whitham. This book was released on 2011-10-18. Linear and Nonlinear Waves available in PDF, EPUB and Kindle. 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.
Introduction to Nonlinear Dispersive Equations
Introduction to Nonlinear Dispersive Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Nonlinear Dispersive Equations write by Felipe Linares. This book was released on 2009-02-21. Introduction to Nonlinear Dispersive Equations available in PDF, EPUB and Kindle. 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.
