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 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.
- Publication:
-
Theoretical and Mathematical Physics
- Pub Date:
- November 2008
- DOI:
- 10.1007/s11232-008-0126-4
- Bibcode:
- 2008TMP...157.1514C
- Keywords:
-
- entire function;
- Painlevé
- transcendent;
- inverse scattering problem