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Book review

Author(s) Segur, H. (ed.)
Tanveer, S. (ed.)
Levine, H. (ed.)
Title Asymptotics beyond all orders
Publisher Plenum
Year of publication 1991
Reviewed by Günter Vojta

This book has been published within the NATO special program on chaos, order, and patterns. It is the proceedings of an advanced research workshop held in La Jolla, California, in January, 1991. The title "asymptotics beyond all orders" refers to a collection of new methods which caused a revolution in asymptotic analysis and its applications in science during the last years. These methods include the influence of transcendentally small terms like exp(-1/e^2) into the analysis of asymptotic power series (semiconvergent series). Such very small corrections can be safely neglected in most applications. However, there exist a number of actual problems for which conventional asymptotic analysis is inadequate. This workshop was devoted to mathematical foundations and diversified applications of the new asymptotology.

The proceedings are divided into ten chapters with altogether thirty papers, most of them original contributions. The topics considered include the principles of asymptotics and Borel summation of series, models of crystal growth, e.g. dendritic crystal growth and directional solidification, pattern formation in viscous fingering, chaotic systems like the forced pendulum, solitons and solitary waves, flow in a porous channel, particle channeling in crystals, and nonlinear problems in optics.

The papers are well written and often supplemented by instructive figures. The authors are mathematicians and, for the most part, physicists many of them being well-known. A detailed subject index is added.

The volume is well produced. It represents a valuable source of information on a professional level for all research workers in mathematics and physics interested in asymptotics and its applications. Libraries in many branches of science and technology should buy it.