ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 34, 35 Brezhnev, Yurii, Kaliningrad State University, Russia Gröbner bases and elliptic solitons Solving of spectral problems with elliptic potentials for ODE’s or system is considered. In its frame the main subproblems are known: 1) search of integrable (finite-gap) potentials, 2) computing of correspondent algebraic curve and 3) problem of covering of torus. We show that they are reduced to pure algebro-geometric problem: solution of polynomial equation system, which can be solved using powerful modern algorithms – Gröbner basis method in theory of polynomial ideals, characteristic sets one and others. New integrable potential with free location of poles has been obtained. Programm package for analytical and numeric Weierstrass’s theory of elliptic functions was created for automation of calculations. Maple programming language is used.