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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 157, Number 2, Pages 175–187
DOI: https://doi.org/10.4213/tmf6273 (Mi tmf6273) 		 
This article is cited in 20 scientific papers (total in 20 papers)

A nonlinear eigenvalue problem

M. Kh. Chankaeva, A. B. Shabatb

a Karachay-Cherkess State University
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (532 kB) Citations (20)
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DOI: https://doi.org/10.4213/tmf6273
Abstract: We reduce the problem of the zeros of an entire function related to the Painlevé I equation to the eigenvalue problem for the Dirichlet problem for a fourth-order bilinear equation. In a simplified case, this problem reduces to the problem of the position of the zeros of theta functions. We then apply the developed general method to the inverse scattering problem.
Keywords: entire function, Painlevé transcendent, inverse scattering problem.
Received: 13.02.2008
English version:
Theoretical and Mathematical Physics, 2008, Volume 157, Issue 2, Pages 1514–1524
DOI: https://doi.org/10.1007/s11232-008-0126-4
Bibliographic databases:
Language: Russian
Citation: M. Kh. Chankaev, A. B. Shabat, “A nonlinear eigenvalue problem”, TMF, 157:2 (2008), 175–187; Theoret. and Math. Phys., 157:2 (2008), 1514–1524
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    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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