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TMF, 2004, Volume 140, Number 2, Pages 230–240 (Mi tmf89)  

This article is cited in 5 scientific papers (total in 5 papers)

Kadomtsev–Petviashvili Equation on the Half-Plane

E. V. Gudkovaa, I. T. Habibullinb

a Ufa State University of Oil and Technology
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We study the boundary value problem for the Kadomtsev–Petviashvili equation on the half-plane $y>0$ with a homogeneous condition along the boundary. We show that the problem can be efficiently solved using the dressing method. We present explicit solutions for particular cases of the boundary value problem.

Keywords: integrability, boundary conditions, Kadomtsev–Petviashvili equation, Lax pair, Marchenko equation, soliton

DOI: https://doi.org/10.4213/tmf89

Full text: PDF file (815 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 140:2, 1086–1094

Bibliographic databases:

Received: 20.11.2003

Citation: E. V. Gudkova, I. T. Habibullin, “Kadomtsev–Petviashvili Equation on the Half-Plane”, TMF, 140:2 (2004), 230–240; Theoret. and Math. Phys., 140:2 (2004), 1086–1094

Citation in format AMSBIB
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\paper Kadomtsev--Petviashvili Equation on the Half-Plane
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\jour Theoret. and Math. Phys.
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\pages 1086--1094
\crossref{https://doi.org/10.1023/B:TAMP.0000036539.35565.1f}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. T. Habibullin, “Truncations of Toda chains and the reduction problem”, Theoret. and Math. Phys., 143:1 (2005), 515–528  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Gurses, M, “Integrable boundary value problems for elliptic type Toda lattice in a disk”, Journal of Mathematical Physics, 48:10 (2007), 102702  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Vereschagin V.L., “Integrable boundary problems for 2D Toda lattice”, Phys Lett A, 374:46 (2010), 4653–4657  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. V. L. Vereshchagin, “Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics”, Theoret. and Math. Phys., 171:3 (2012), 792–799  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    5. V. L. Vereshchagin, “Explicit Solutions of Boundary-Value Problems for $(2+1)$-Dimensional Integrable Systems”, Math. Notes, 93:3 (2013), 360–372  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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