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Nonlinear science. Emergence and dynamics of coherent structures. With contributions from Mads Peter Sørensen and Peter Leth Christiansen. (English) Zbl 0927.35002

Oxford Applied and Engineering Mathematics 1. Oxford: Oxford University Press (ISBN 0-19-850107-2/hbk). xvii, 474 p. (1999).
The book presents a suggestive panoramic view of the history and experimental motivation of nonlinear phenomena. The problems at the end of each chapter are a good training to get a better understanding of the topics and suggest new directions of research.
The basic unperturbed nonlinear models are exhaustively studied in the mathematical and experimental contexts, ranging from continuous to discrete models. A very basic and useful presentation with the applications of the perturbation methods is also analyzed.
Due to the fundamental role of the numerical studies in the development of the nonlinear science, a section devoted to them should have been perhaps included.
I recommend this book as a reference-text for undergraduate students of last year as well as a basic book for an interdisciplinary Ph.D. course in natural sciences and engineering. The book is a basic one for all the bridge studies with biology as the biophysics and biocomputing, and, in particular, for the emerging area of astrobiology.
Reviewer: L.Vazquez (Madrid)

MSC:

35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
35K55 Nonlinear parabolic equations
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q58 Other completely integrable PDE (MSC2000)
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