Geodesic
Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 430-437

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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. 
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     author = {V. L. Vereshchagin},
     title = {Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {430--437},
     publisher = {mathdoc},
     volume = {171},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a5/}
}
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V. L. Vereshchagin. Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 430-437. http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a5/