In the example of the SchrÃ¶dinger/KdV equation, we treat the theory as equivalence of two concepts of Liouvillian integrability: quadrature integrability of linear differential equations with aâ€¦ (More)

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for exactly solvable potentials and their spectralâ€¦ (More)

Uniformisation, Schwarzâ€™s equation and a conjecture of Whittaker for the Burnside algebraic curve are discussed. 1 Permanent address: Theoretical Physics Department, Kaliningrad State University, A.â€¦ (More)

New exact solvable elliptic potentials with free constants for the spectral problems of the third order are found. A time dependence of such potentials gives their isospectral deformations andâ€¦ (More)

TheWeierstrass elliptic functions can be parameterised using either lattice generators or invariants. Most presentations adopt the former approach. In this paper the authors give formulae that enableâ€¦ (More)

The Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the frameworkâ€¦ (More)

Uniformization, Schwarzâ€™s/Fuchsian equations, accessory parameters, and a conjecture of Whittaker for the Burnside algebraic curve are discussed. 1Current address: Department of Mathematics andâ€¦ (More)

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for the exact solvable potentials and their spectralâ€¦ (More)

Uniformisation, Schwarzâ€™s (Fuchsian) equation and a conjecture of Whittaker for the Burnside algebraic curve are discussed. Permanent address : Theoretical Physics Department, Kaliningrad Stateâ€¦ (More)

We consider the solution of spectral problems with elliptic potentials in the framework of the Hermite ansatz. We show that the search for potentials and their spectral characteristics is reduced toâ€¦ (More)