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Exactly Solvable Models in Mathematical Physics
August 3-8, 1998
South Ural State University
Chelyabinsk, Russia

Organizers
Anjan Kundu, Alexander B. Borisov, Arlen M. Il'in, Igor G. Korepanov, Vladimir E. Korepin, Yuri G. Stroganov

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Harmonic inverse mean curvature surfaces and localized Painleve III transcendents
by
Victor Novokshenov
Institute of Mathematics in Ufa

Recently found localized solutions of the third Painleve equation demonstrate an exponential decay at infinity together with rapid oscillations at finite distance. They were used for description of a shock-wave type behavior of the Sine-Gordon wave packets. Now a new application has been found in a framework of constant mean curvature (CRC) surfaces in R3. A number of examples of compact harmonic inverse CRC surfaces of revolution are constructed in terms of localized Painleve III transcendents.

Date received: February 28, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaw-10.