arXiv subjects
Publications and source records attributed to S. V. Agapov.
In this paper we show that the one-dimensional Schrödinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In case of the Schrödinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker--Akhiezer function
In this paper the magnetic geodesic flow on a 2-torus is considered. We study a semi-hamiltonian quasi-linear PDEs which is equivalent to the existence of polynomial in momenta first integral of magnetic geodesic flow on fixed energy level. It is known that diagonal metric associated with this system is Egorov one if degree of the first integral is equal to 2 or 3. In this paper we prove this fact in the case of existence of the first integral of any degree.