A nonlinear eigenvalue problem
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 fourthorder 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.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 November 2008
 DOI:
 10.1007/s1123200801264
 Bibcode:
 2008TMP...157.1514C
 Keywords:

 entire function;
 Painlev&eacute;
 transcendent;
 inverse scattering problem