Elliptic Solitons and Groebner Bases

Abstract

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 spectral characteristics is reduced to a system of polynomial equations solvable by the Gröbner bases method and others. New integrable potentials and corresponding solutions of the Sawada-Kotera, Kaup-Kupershmidt, Boussinesq equations and others are found.

18 pages, no figures, LaTeX'2e

References in corpus (3)

• Algebro-Geometric Solutions of the Boussinesq Hierarchy
• On the explicit solutions of the elliptic Calogero system
• Elliptic Solitons with Free Constants and their Isospectral Deformations

Cited by in corpus (1)

• Lamé polynomials, hyperelliptic reductions and Lamé band structure