Algebraic geometry and mathematical physics

The one-dimensional Cartewega-de-Fries equation is studied. The method of the inverse problem is used for constructing periodic and quasiperiodic solutions of this equation. The stationary solutions of this equation are shown to be connected with the Riemann surface and to be quite an integrable hamiltonian system. The inverse problem method is generalized to some space-two-dimensional systems. Holomorphic stratifications over the Riemann surfaces are considered and exact solutions of the quasipotential equation are found