On calculation of new elliptic solutions of the spectral problem for the finite-gap Schrödinger operator

Abstract:
On the basis of finite-gap equations and the rational function representation we have obtained algebraic relations determining all solutions of the spectral problem for the finite-gap Schrödinger operator. The complete system of one-gap elliptic potentials including together with even (specifically the Lame) add elliptic potentials is calculated.