Nonlinear Science: gence and Dynamics of Coherent Structures

Hardcover | August 24, 2005

byAlwyn Scott

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Much mathematical modelling has involved the assumption that physical systems are approximately linear, leading to the construction of equations which, although relatively easy to solve, are unrealistic and overlook significant phenomena. Models assuming nonlinear systems, however, lead to theemergence of new structures that reflect reality much more closely. This second edition of Nonlinear Science, covers several important areas of nonlinear science, and places a strong emphasis on applications to realistic problems. It includes numerous new topics such as empirical results in molecular dynamics, solid-state physics, neuroscience, fluid dynamics, andbiophysics; numerous new exercises and solutions; updated sections on nerve impulse dynamics, quantum-theory of pump-probe measures, and local modes on lattices. With over 350 problems, including hints and solutions, this is an invaluable resource for graduate students and researchers in the appliedsciences, mathematics, biology, physics and engineering.This is the latest title in the Oxford Texts in Applied and Engineering Mathematics, which includes a range of texts from the undergraduate through to the graduate level. Most titles should be based on taught courses which explain the mathematical or computational techniques required for theresolution of fundamental applied problems. Other books in the series include: D. W. Jordan and P. Smith: Nonlinear ordinary differential equations: an introduction to dynamical systems 3rd Edition; I. J. Sobey: Introduction to interactive boundary layer theory; A. B. Tayler: Mathematical Models inApplied Mechanics (reissue); Ramdas Ram-Mohan: Finite Element and Boundary Element Applications in Quantum Mechanics; Lapeyre et al: Introduction to Monte-Carlo Methods for Transport and Diffusion Equations; Isaac Elishakoff and Yong Jin Ren: Finite Element Methods for Structures with LargeStochastic Variations

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Much mathematical modelling has involved the assumption that physical systems are approximately linear, leading to the construction of equations which, although relatively easy to solve, are unrealistic and overlook significant phenomena. Models assuming nonlinear systems, however, lead to theemergence of new structures that reflect re...

Alywn Scott is an Emeritus Professor at the Department of Mathematics at the University of Arizona and a Consultant at the Department of Informatics and Mathematical Modelling at the Technical University of Denmark. He is the editor of the forthcoming Encyclopedia of Nonlinear Science (Taylor and Francis (Routledge), New York). He is...

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Format:HardcoverDimensions:496 pages, 9.21 × 6.14 × 1.2 inPublished:August 24, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198528523

ISBN - 13:9780198528524

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Table of Contents

1. The Birth of a Paradigm2. Linear Wave Theory3. The Classical Soliton Equations4. Reaction-Diffusion Systems5. Nonlinear Lattices6. Inverse Scattering Methods7. Peturbation Theory8. Quantum Lattice Solitons9. Looking AheadBibliographyIndex

Editorial Reviews

'..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.....I recommend this book as areference-text for undergraduate students of last year as well as a basic book for an interdisciplinary P.H.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 ofastrobiology.' MATH