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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 140, Number 2, Pages 230–240
DOI: https://doi.org/10.4213/tmf89 (Mi tmf89) 		 
This article is cited in 7 scientific papers (total in 7 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
Full-text PDF (815 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf89
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.
Received: 20.11.2003
English version:
Theoretical and Mathematical Physics, 2004, Volume 140, Issue 2, Pages 1086–1094
DOI: https://doi.org/10.1023/B:TAMP.0000036539.35565.1f
Bibliographic databases:
Language: Russian
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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  • https://doi.org/10.4213/tmf89
  • https://www.mathnet.ru/eng/tmf/v140/i2/p230
    • This publication is cited in the following 7 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
    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
    3. 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
    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. 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
    6. 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
    7. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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