This article is cited in 20 papers

A nonlinear eigenvalue problem

M. Kh. Chankaev^a, A. B. Shabat<sup>b

a</sup> Karachay-Cherkess State University
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

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

DOI: 10.4213/tmf6273

 English version: Theoretical and Mathematical Physics, 2008, 157:2, 1514–1524

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