Inverse problem for 3-rd order operators under the 3-point Dirichlet conditions

Abstract

We solve an inverse problem for a third order differential operator under the 3-point Dirichlet conditions. The third-order operator is an $L$-operator in the Lax pair for the good Boussinesq equation. We construct the mapping from the set of the coefficients to the set of spectral data. This mapping is an analytic bijection on a neighborhood of the zero.