This article is cited in 2 papers

Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics

V. L. Vereshchagin

Institute of Mathematics with Computing Center, Ufa Science Center, RAS, Ufa, Russia

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.

Keywords: two-dimensional Toda chain, Kadomtsev–Petviashvili equation, integrable boundary-value problem.

Received: 17.07.2011

DOI: 10.4213/tmf6932

 English version: Theoretical and Mathematical Physics, 2012, 171:3, 792–799

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