Elliptic Solitons and Groebner Bases

Details Elliptic Solitons and Groebner Bases Elliptic Solitons and Groebner Bases

2000-07-20

arxiv.org/abs/nlin/0007028v4

Journ. Math. Phys (2004), v.45(2), 696-712

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, no figures, LaTeX'2e

Scientific paper

10.1063/1.1633353

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.

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