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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.

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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}
}

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14 pages