Partial differential equations and solitary waves theory
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.
scientific article; zbMATH DE number 5549978