Customer Reviews

Nonlinear Science: Emergence and Dynamics of Coherent Structures (Oxford Texts in Applied and Engineering Mathematics 8)

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I am currently taking a couse based on this book and am fairly impressed. The book is very interesting to read and Scott occasionally adds some humourous bits or interesting facts that help out alot. However on the mathematics side alot of steps are skipped which makes it difficult to follow at times. However there are a load of references given for each chapter, so if you do get stuck you can go to the source. Overall an interesting book, but not the best for an introduction to the material.

This book has a very important mission. It is to break through the conventional approach to science and engineering in which mathematical representations of systems are almost always linearized. When faced with a nonlinear equation today, most students immediately race to solve the problem with a computer, thereby missing the opportunity to ever observe new qualitative structures that emerge from the nonlinear mathematics. To go past this bottleneck, the author starts with a historical review of the experimental and theoretical developments in nonlinear science which often amazes the students of today since many discoveries were made more than 2 centuries ago! The student is then guided through the relevant linear theory and gently introduced to the classical nonlinear equations that have produced soliton waves which have even made their way into Star Trek! The notion that a wave equation is not necessary to produce traveling wave solutions in is another striking development, which is a critical approach to the propagation of impulses in nerve fibers, for example. Yet the concept itself is introduced by examining the behavior of a candle!
The skills needed for the Backlund transformation, inverse scattering and perturbation methods are introduced, but there are always numbers of well-thought-out problems that cover the basics as well as the more detailed concepts in each chapter.
What is particularly impressive about this book is the wide range of nonlinear phenomena in an incredible number of disciplines that exhibit similar nonlinear behavior. For those who search for cross-disciplinary applications, this book is a marvelous compendium of information.
This text is extremely well written. It can easily be used as a text in a seminar-style class, where one can sense the author's presence as the guiding hand behind the material.