Scott, Alwyn [Sørensen, Mads Peter; Christiansen, Peter Leth] 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) Cited in 2 ReviewsCited in 57 Documents 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) Keywords:nonlinear dynamics; soliton; diffusion; lattice PDFBibTeX XMLCite \textit{A. Scott}, Nonlinear science. Emergence and dynamics of coherent structures. With contributions from Mads Peter Sørensen and Peter Leth Christiansen. Oxford: Oxford University Press (1999; Zbl 0927.35002)