Title: On a class of exact solutions of the Ishimori equation

Abstract: In report we discuss a construction class of particular solutions of the Ishimori equation.  This equation is known as the spatially two-dimensional version of the Heisenberg equation. 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, we found an essentially new class of solutions to the Ishimori equation. This results published in [1]

Additionally, a certain method for classifying a two-dimensional Toda-type lattice is proposed.

1. R.N. Garifullin, I.T. Habibullin On a class of exact solutions of the Ishimori equation// Physica D: Nonlinear Phenomena 480 (2025) 134746 DOI: 10.1016/j.physd.2025.134746 arXiv:2412.18195