EXTENDED CLASS OF DUBROVINS EQUATIONS RELATED TO THE ONE-DIMENSIONAL QUANTUM 3-BODY PROBLEM

The relation of the quantum 1D three-body problems with zero-range int eraction to the matrix Riemann-Hilbert problem with meromorphic coeffi cient is shown. The solution of this problem is discussed using the ex act analytic diagonalization of the coefficient. The problem is reduce d to the boundary value problem on the Riemann surface. The solution o f this problem is expressed in terms of the Riemann theta-functions. A n extended class of integrable Dubrovin's type ordinary differential e quations related to the one-dimensional quantum three-body problem is derived.