Theoretical Physics, Mathematical Physics, Waves & Wave Mechanics, Optics - General & Miscellaneous, Mathematics - Applied

KdV '95

Name: KdV '95
Author: and named after Korteweg and de Vries
ISBN: 9780792334675

by and named after Korteweg and de Vries

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Overview

Exactly one hundred years ago, in 1895, G. de Vries, under the supervision of D. J. Korteweg, defended his thesis on what is now known as the Korteweg-de Vries Equation. They published a joint paper in 1895 in the Philosophical Magazine, entitled 'On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave', and, for the next 60 years or so, no other relevant work seemed to have been done. In the 1960s, however, research on this and related equations exploded. There are now some 3100 papers in mathematics and physics that contain a mention of the phrase 'Korteweg-de Vries equation' in their title or abstract, and there are thousands more in other areas, such as biology, chemistry, electronics, geology, oceanology, meteorology, etc. And, of course, the KdV equation is only one of what are now called (Liouville) completely integrable systems. The KdV and its relatives continually turn up in situations when one wishes to incorporate nonlinear and dispersive effects into wave-type phenomena. This centenary provides a unique occasion to survey as many different aspects of the KdV and related equations. The KdV equation has depth, subtlety, and a breadth of applications that make it a rarity deserving special attention and exposition.

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Booknews

Proceedings of the symposium held in April 1995 to commemorate the centennial of the publication of the equation by Korteweg and de Vries (KdV equation) in their famous 1895 paper "On the Change of Form of Long Waves Advancing in a Rectangular Canal and on a New Type of Long Stationary Waves." The plenary lectures and invited contributions reflect the application of many branches of mathematics, such as analysis, differential geometry, algebraic geometry, topology, and infinite-dimensional algebraic structures; as well as numerous applications in physics, e.g., in statistical mechanics, point mechanics, hydrodynamics, optics, and field theory. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)