Inverse problem for the divisor of the good Boussinesq equation
Abstract
A third-order operator with periodic coefficients is an L-operator in the Lax pair for the Boussinesq equation on a circle. The projection of the divisor of the Floquet solution poles for this operator coincides with the spectrum of the three-point Dirichlet problem. The sign of the norming constant of the three-point problem determines the sheet of the Riemann surface on which the pole lies. We solve the inverse problem for a third-order operator with three-point Dirichlet conditions when the spectrum and norming constant are known. We construct a mapping from the set of coefficients to the set of spectral data and prove that this mapping is an analytic bijection in the neighborhood of zero.
Fields of Study & Subjects
Geometry and complex manifolds
Holomorphic and Operator Theory
Functional Equations Stability Results
Publication details
- Journal / source
- Applicable Analysis
- Publisher
- Informa UK Limited
- Volume
- 105
- Issue
- 15
- Pages
- 1–51
- Publication date
- 11 May 2026
- Language
- EN