On a class of exact solutions of the Ishimori equation

2024/12/24 by R. N. Garifullin, Garifullin, Rustem N., I. T. Habibullin +1 · 2 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2412.18195

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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