(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
The familiar wave equation is the most fundamental hyperbolic partial differential equation. Other hyperbolic equations, both linear and nonlinear, exhibit many wave-like phenomena. The primary theme of this book is the mathematical investigation of such wave phenomena.
The book is geared toward a wide audience interested in PDEs. Prerequisite to the text are some real analysis and elementary functional analysis. It would be suitable for use as a text in PDEs or mathematical physics at the advanced undergraduate and graduate level.
Translations of Mathematical Monographs
(Iwanami Series in Modern Mathematics); 2000; approximately 194
A great deal of progress has been made in the modelling and understanding of processes with nonlinear dynamics, even when only time series data are available. The so-called reconstruction theory deals with making nonlinear dynamical models from data and is at the heat of this improved understanding. This edited book, presenting chapters contributed by leading researchers in the field, gives a thorough and comprehensive survey of theory and methods topics describing the state of the art in nonlinear dynamical reconstruction theory.
August 2000, approx. 400 pages, 85 illustrations, hardcover.
Discusses a range of topics: diffusion population dynamics, autonomous differential equations and the stability of ecosystems, biogeography, pharmokinetics, biofluid mechanics, cardiac mechanics, and the spectral analysis of heart sounds using FFT techniques. Includes new chapters on epidemiology, including modelling the spread of AIDS through a population. The reader is aided by many exercises that examine key points and extend the presentation in the body of the text.
Cambridge Studies in Mathematical Biology 16
1999 240 pages
In less than 100 pages, this book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity.
Pedregal introduces the reader to Young measures as an important took in solving vector variational techniques. In addition, many valuable references are included to direct the reader to other important research.
2000. xii+99 pages, softcover.
Beginning with ordinary language models or realistic mathematical models of physics or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of the text is devoted to careful derivations of implicit function theorems, methods of averaging, and quasi-static state approximation methods. For the second edition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.
2000, app 344 pages, 73 illustrations, hardcover
Applied Mathematical Sciences, Volume 94.
This second edition of a classic mathematical biology book deals with the dynamics of professes that repeat themselves regularly. This cycle of change is a ubiquitous principle of organization in living systems. This new edition addresses areas in biomathematics that have come to fruition since 1980. The author, a lead in the field, offers valuable insights into the important areas of future development in nonlinear dynamics in the natural sciences.
August 2000, approximately 750 pages, 290 illustrations
Hardcover ISBN 0-387-52528-9
Interdisciplinary Applied Mathematics Volume 12
In the past hundred years investigators have learned the significance of complex behaviour in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.
This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behaviour in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers.
Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike.
World Scientific Series on Nonlinear Science, Series A - Volume 25