English

Elliptic Solitons and Groebner Bases

Exactly Solvable and Integrable Systems 2009-10-31 v4

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 Gr\"obner bases method and others. New integrable potentials and corresponding solutions of the Sawada-Kotera, Kaup-Kupershmidt, Boussinesq equations and others are found.

Keywords

Cite

@article{arxiv.nlin/0007028,
  title  = {Elliptic Solitons and Groebner Bases},
  author = {Yurii V. Brezhnev},
  journal= {arXiv preprint arXiv:nlin/0007028},
  year   = {2009}
}

Comments

18 pages, no figures, LaTeX'2e

R2 v1 2026-07-22T18:07:10.499Z