34 citations · 56 across the 7 of their papers we have counts for
7 papers
Solution of the Jacobi inversion problem on non-hyperelliptic curves
Julia Bernatska, Dmitry Leykin
In this paper we propose a method of solving the Jacobi inversion problem in terms of multiply periodic functions, also called Kleinian functions. This result is based…
Multi-variable sigma-functions: old and new results
Victor Buchstaber, Victor Enolski, Dmitry Leykin
We consider multi-variable sigma function of a genus hyperelliptic curve as a function of two group of variables -jacobian variables and parameters of the curve. In the theta-f…
On Regularization of Second Kind Integrals
Julia Bernatska, Dmitry Leykin
We obtain expressions for second kind integrals on non-hyperelliptic -curves. Such a curve possesses a Weierstrass point at infinity which is a branch point where all sheets…
On degenerate sigma-functions of genus two
Julia Bernatska, Dmitry Leykin
We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus sigma-function and elementary functions as solutions of a system of linear PDEs satisfied…
Multi-Dimensional Sigma-Functions
V. M. Buchstaber, V. Z. Enolski, D. V. Leykin
In 1997 the present authors published a review (Ref. BEL97 in the present manuscript) that recapitulated and developed classical theory of Abelian functions realized in terms of mu…
Hyperelliptic addition law
Victor Buchstaber, Dmitry Leykin
We construct an explicit form of the addition law for hyperelliptic Abelian vector functions and . The functions and form a basis in the field of hyperelli…
Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates
J C Eilbeck, V Z Enol'skii, V B Kuznetsov +1
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a gene…