UK Nonlinear News, August 2000


Modulated Waves: Theory and Applications

Lev A Ostrovsky and Alexander S Potapov

Reviewed by Professor G. Rowlands

John Hopkins University Press, 49.5
ISBN 0-8018-5970-4.

The book presents a thorough treatment of modulated waves, both linear and non-linear, that is waves whose amplitude and phase change with position and time.

Though throughout the book the underlying treatment is mathematical the basic concepts are well introduced using physical applications.

The first 150 or so pages are devoted to the phenomena of linear dispersion of waves propagating in uniform media. Besides the usual theory based on expansion in Fourier modes, Lagrangian formulation is introduced which is then used to give a mathematical treatment of Geometric Optics.

The next 50 pages deal with the application of the W.K.B. method to treat wave propagation in inhomogeneous media.

Finally, the last 150 pages are used to introduce some non-linear concepts. This section begins with an account of how the physical models introduced in the first half of the book have a common non-linear aspect modelled by the K de V, Burger's and the sinc-Gordon equations. The non-linear aspects of these equations are then explored by studying travelling wave solutions.

A chapter is devoted to the derivation and illustration of basic properties of the non-linear Schrodinger equation as used to describe the propagation of non-linear quasi-harmonic waves. The emphasis is on the basic properties of the equation and reference only is made to the soliton theory of exact solutions.

Finally in the last chapter the authors bring together the work discussed in earlier chapters to give an interesting introduction to the theory of non-linear wave propagation in non-uniform media.

Throughout, the emphasis is on an analytic treatment and the book gives plenty of examples of how simple analytic techniques can be applied to bring out the essential physical behaviour of wave propagation.

Each chapter concludes with some historic remarks and comments, exercises and a good list of references.

The book could be well used as a standard book for a postgraduate course in applied mathematics or theoretical physics on waves. The earlier chapters could be used at an undergraduate level as an introduction to wave dispersion.

A listing of books reviewed in UK Nonlinear News is available.

UK Nonlinear News thanks the John Hopkins University Press for providing a review copy of this book.


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