## Extended class of Dubrovin’s equations related to the one-dimensional quantum three-body problem.(English)Zbl 0897.47055

Summary: The relation of the quantum one-dimensional three-body problems with zero-range interaction to the matrix Riemann-Hilbert problem with meromorphic coefficient is shown. The solution of this problem is discussed using the exact analytic diagonalization of the coefficient. The problem is reduced to the boundary value problem on the Riemann surface. The solution of this problem is expressed in terms of the Riemann theta-functions. An extended class of integrable Dubrovin’s type ordinary differential equations related to the one-dimensional quantum three-body problem is derived.

### MSC:

 47N50 Applications of operator theory in the physical sciences 81U10 $$n$$-body potential quantum scattering theory 30E25 Boundary value problems in the complex plane
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### References:

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