ON THE GEOMETRY OF ELLIPTIC SOLITONS

We study special algebraic curves being a covering over tori and associated with elliptic solitons. To describe the cover, we use an ansatz for the elliptic Baker-Akhiezer functions which accentuates the work of Hermite. We give a description of the elliptic solitons yielded by two-gap Lame and Treibich-Verdier potentials; we also consider three and four-gap Lame potentials and the Halphen equation with n = 4. Examples of elliptic solutions for integrable dynamical systems are constructed against the background of the developed approach.