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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 171, Number 3, Pages 430–437
DOI: https://doi.org/10.4213/tmf6932 (Mi tmf6932) 		 
This article is cited in 2 scientific papers (total 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
Full-text PDF (383 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf6932
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
English version:
Theoretical and Mathematical Physics, 2012, Volume 171, Issue 3, Pages 792–799
DOI: https://doi.org/10.1007/s11232-012-0075-9
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6932
  • https://doi.org/10.4213/tmf6932
  • https://www.mathnet.ru/eng/tmf/v171/i3/p430
    • This publication is cited in the following 2 articles:
    1. Dubrovsky V.G. Topovsky V A., “Multi-Soliton Solutions of Kp Equation With Integrable Boundary Via Partial Differential -Dressing Method”, Physica D, 428 (2021), 133025  crossref  mathscinet  isi  scopus
    2. Dubrovsky V.G. Topovsky V A., “Multi-Lump Solutions of Kp Equation With Integrable Boundary Via Partial Derivative-Dressing Method”, Physica D, 414 (2020), 132740  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:89
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