Integrable boundary conditions for nonlinear partial differential equations
by
Ismagil Habibullin
Ufa Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky str., Ufa, Russia

At present classes of boundary conditions are known for integrable nonlinear partial differential equations and lattice equations with two independent variables, in both classical and quantum versions, compatible with the integrability property. In the last decade the subject has become rather popular, various approaches were worked out and applied succesfully. An effective method to investigate boundary value problems for integrable 1+1 dimensional nonlinear equations is based on the symmetry approach. The symmetry test established there allows one, in principle, to describe the complete set of boundary conditions for the given equation (or cutting conditions in the case of lattices), compatible with its integrability property. However, the initial boundary value problem for integrable systems with more than two independent variables remains less studied. In the talk an attempt to generalize the symmetry test to the multi-dimensional case will be discussed. As a touchstone we take a very well studied two-dimensional integrable phenomena - 2D Toda lattice equation.

Date received: May 29, 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-28.