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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 2, Pages 71–83
DOI: https://doi.org/10.4213/faa109 (Mi faa109) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Boundary Conditions for Multidimensional Integrable Equations

I. T. Habibullina, E. V. Gudkovab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b Ufa State University of Oil and Technology
Full-text PDF (202 kB) Citations (12)
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DOI: https://doi.org/10.4213/faa109
Abstract: We suggest an efficient method for finding boundary conditions compatible with integrability for multidimensional integrable equations of Kadomtsev–Petviashvili type. It is observed in all known examples that imposing an integrable boundary condition at a point results in an additional involution for the $t$-operator of the Lax pair. The converse is also likely to be true: if constraints imposed on the coefficients of the $t$-operator of the $L$-$A$ pair result in a broader group of involutions of the $t$-operator, then these constraints determine integrable boundary conditions.
New examples of boundary conditions are found for the Kadomtsev–Petviashvili and modified Kadomtsev–Petviashvili equations.
Keywords: integrable equation, Hamiltonian structure, Kadomtsev–Petviashvili equation, Lax pair.
Received: 11.11.2002
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 2, Pages 138–148
DOI: https://doi.org/10.1023/B:FAIA.0000034044.01773.dd
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: I. T. Habibullin, E. V. Gudkova, “Boundary Conditions for Multidimensional Integrable Equations”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 71–83; Funct. Anal. Appl., 38:2 (2004), 138–148
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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