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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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Singular solution of the Liouville equation under perturbation
by
Leonid Kalyakin
Institute of Mathematics, Ufa, Sci. Centre of Russian Academy of Sciences

The Cauchy problem for the Liuoville equation under small perturbation \phitt - \phixx + 2exp(\phi) = \epsilonF[\phi], 0 < \epsilon << 1 is considered. Unperturbed solution is represented in the form \phi0 = ln(r+'r-'[r++r-]-2), r +/- = r +/- (s +/- ), s +/- = x +/- t and one has a singularity along the line r+(x+t) + r(x-t) = 0. The perturbation operator F[\phi] is a smooth function of the \phi and the first derivative \phix. An asymptotic expansion of the perturbed solution \phi(x, t;\epsilon) as \epsilon --> 0 is constructed.

Date received: May 4, 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-23.