Integrable boundary conditions for (2+1)-dimensional models of mathematical physics |
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Authors: | V. L. Vereshchagin |
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Affiliation: | 1. Institute of Mathematics with Computing Center, Ufa Science Center, RAS, Ufa, Russia
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Abstract: | We consider the question of integrable boundary-value problems in the examples of the two-dimensional Toda chain and Kadomtsev-Petviashvili equation. We discuss the problems that are integrable from the standpoints of two basic definitions of integrability. As a result, we propose a method for constructing a hierarchy of integrable boundary-value problems where the boundaries are cylindric surfaces in the space of three variables. We write explicit formulas describing wide classes of solutions of these boundary-value problems for the two-dimensional Toda chain and Kadomtsev-Petviashvili equation. |
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