4 research outputs found
Elliptic Solitons and Groebner Bases
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 Gr\"obner bases method and others. New
integrable potentials and corresponding solutions of the Sawada-Kotera,
Kaup-Kupershmidt, Boussinesq equations and others are found.Comment: 18 pages, no figures, LaTeX'2