Partial differential equations and solitary waves theory
type: Item
instance of: scholarly article
title: Partial differential equations and solitary waves theory
zbMATH Open document ID: 1175.35001
author: Abdul-Majid Wazwaz
published in: Nonlinear Physical Science
publication date: 2009-04-30T00:00:00Z
review text: This book is devoted to the study of classical and new methods for solving partial differential equations (linear and nonlinear). Only analytical methods are described. They lead to explicit function solutions unlike discretization methods such as finite differences or finite elements methods giving solutions on discrete sets. Adomian decomposition method is the main technique very clearly and rigorously detailed in this book with applications to a lot of concrete partial differential equations. In further chapters, solitons and compactons are used for obtaining solitary waves equations. Many classical partial differential equations are entirely solved by means of these methods. This work clearly explains the methods and their applications to concrete equations. It can be read by undergraduate and graduate students. But it will be also very useful for researchers in applied mathematics and engineering because it suggests new and powerful techniques avoiding discretization and linearization I warmly recommend this reference book for its simplicity and its rigour.
reviewed by: Yves Cherruault
Mathematics Subject Classification ID: 35-01
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35G05
Mathematics Subject Classification ID: 35G30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 5549978
zbMATH Keywords: partial differential equations
zbMATH Keywords: Adomian decomposition method
zbMATH Keywords: solitons
zbMATH Keywords: solitary waves theory
zbMATH Keywords: variational iteration method
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5549978