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TMF, 2012, Volume 171, Number 3, Pages 430–437 (Mi tmf6932)  

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

DOI: https://doi.org/10.4213/tmf6932

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

Bibliographic databases:

Received: 17.07.2011

Citation: V. L. Vereshchagin, “Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics”, TMF, 171:3 (2012), 430–437; Theoret. and Math. Phys., 171:3 (2012), 792–799

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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