On a class of exact solutions of the Ishimori equation
Exactly Solvable and Integrable Systems
2025-04-15 v2 Mathematical Physics
math.MP
Abstract
In this paper, a class of particular solutions of the Ishimori equation is found. This equation is known as the spatially two-dimensional version of the Heisenberg equation, which has important applications in the theory of ferromagnets. It is shown that the two-dimensional Toda-type lattice found earlier by Ferapontov, Shabat and Yamilov is a dressing chain for this equation. Using the integrable reductions of the dressing chain, the authors found an essentially new class of solutions to the Ishimori equation.
Cite
@article{arxiv.2412.18195,
title = {On a class of exact solutions of the Ishimori equation},
author = {Rustem N. Garifullin and Ismagil T. Habibullin},
journal= {arXiv preprint arXiv:2412.18195},
year = {2025}
}
Comments
14 pages