Harmonic Analysis Method for Nonlinear Evolution Equations

First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

This monograph provides a comprehensive overview on a class of nonlinear dispersive equations, such as nonlinear Schrodinger equation, nonlinear Klein–Gordon equation, KdV equation as well as the Navi

The Adomian decomposition method (ADM) is a semi-analytical method capable of solving partial and ordinary nonlinear differential equations. This book shows how ADM can be used to solve problems formu

Any engineer or scientist taking part in a computational project or involved in any computational science and engineering academic program will benefit from this book. Because the examples area is so

Philippe Benilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations an

The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations

Solitons have been of considerable interest to mathematicians since their discovery by Kruskal and Zabusky. This book brings together several aspects of soliton theory currently only available in research papers. Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ∂ method. Thus, this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decompos

Reporting a novel breakthrough in the identification and investigation of solvable and integrable nonlinearly coupled evolution ordinary differential equations (ODEs) or partial differential equations (PDEs), this text includes practical examples throughout to illustrate the theoretical concepts. Beginning with systems of ODEs, including second-order ODEs of Newtonian type, it then discusses systems of PDEs, and systems evolving in discrete time. It reports a novel, differential algorithm which can be used to evaluate all the zeros of a generic polynomial of arbitrary degree: a remarkable development of a fundamental mathematical problem with a long history. The book will be of interest to applied mathematicians and mathematical physicists working in the area of integrable and solvable non-linear evolution equations; it can also be used as supplementary reading material for general applied mathematics or mathematical physics courses.

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, bu

In this book we present a significant part ofthe material given in an autumn school on "Nonlinear Analysis and Differential Equations," held at the CMAF (Centro de Matematica e Aplica

This concise and widely referenced monograph has served as a text for generations of advanced undergraduate math majors and graduate students. Prepared with an eye toward the needs of applied mathemat

This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoin

The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations an

The first book applying HBFEM to practical electronic nonlinear field and circuit problems • Examines and solves wide aspects of practical electrical and electronic nonlinear field and circuit problem