This volume contains the contributions to a symposium held at Gatlinburg, Tennessee, under the auspices of the Oak Ridge National Laboratory, in April, 1971. In the past, these proceedings had appeared as a supplement to the Journal of Cellular Physiology. Due to the nature of the subject ma terial and the relevance of the topic of the symposium to the readers of BIOMEMBRANES, it was agreed by the organizers of the symposium to publish the contributions of the partici pants as a separate volume in BIOMEMBRANES. It had been originally envisaged that, from time to time, the proceedings of a conference whose subject matter was directly related to the scope of this series would be included. The proceedings are being published exactly as they have been submitted to the Editor without the usual editorial re V1S10n. This is being done to increase the speed of publica tion. For the same rOeason, no indices have been provided since the time needed to prepare an adequate subject index would have unnecessarily delayed publication. Included in the proceedings are short reports of a number of workshops that were held during the conference. The editor has received excellent cooperation from both the organizers of the conference and the several contributors to this volume. If the experiment is a success, it is thanks to their promptness.
Many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries and non-linear Schrodinger equations are reductions of the self-dual Yang-Mills equation. This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It supports two central theories: that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and that twistor theory provides a uniform geometric framework for the study of Backlund transformations, the inverse scattering method, and other such general constructions of integrability theory. The book will be useful to researchers and graduate students in mathematical physics.
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