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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 131, Number 3, Pages 389–406
DOI: https://doi.org/10.4213/tmf336 (Mi tmf336) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments

A. V. Pereskokov

Moscow Power Engineering Institute (Technical University)
Full-text PDF (286 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf336
Abstract: We consider the eigenvalue problem for the two-dimensional Schrödinger equation containing an integral Hartree-type nonlinearity with an interaction potential having a logarithmic singularity. Global asymptotic solutions localized in the neighborhood of a line segment in the plane are constructed using the matching method for asymptotic expansions. The Bogoliubov and Airy polarons are used as model functions in these solutions. An analogue of the Bohr–Sommerfeld quantization rule is established to find the related series of eigenvalues.
Received: 11.10.2001
English version:
Theoretical and Mathematical Physics, 2002, Volume 131, Issue 3, Pages 775–790
DOI: https://doi.org/10.1023/A:1015923406662
Bibliographic databases:
Language: Russian
Citation: A. V. Pereskokov, “Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments”, TMF, 131:3 (2002), 389–406; Theoret. and Math. Phys., 131:3 (2002), 775–790
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    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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