Geodesic
A~nonlinear eigenvalue problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 175-187

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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. 
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     author = {M. Kh. Chankaev and A. B. Shabat},
     title = {A~nonlinear eigenvalue problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {175--187},
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     volume = {157},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a1/}
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M. Kh. Chankaev; A. B. Shabat. A~nonlinear eigenvalue problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 175-187. http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a1/