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arXiv · 2412.18195

On a class of exact solutions of the Ishimori equation

Rustem N. Garifullin·Ismagil T. Habibullin
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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.

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Rustem N. Garifullin, Ismagil T. Habibullin. 2025-04-14. On a class of exact solutions of the Ishimori equation. https://doi.org/10.1016/j.physd.2025.134746

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