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arXiv · 2403.18165

A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions

T. Valchev
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Abstract

We consider a matrix nonlinear partial differential equation that generalizes Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet equation is completely integrable with a linear bundle Lax pair related to the pseudo-unitary algebra. This allows us to explicitly derive particular solutions by using dressing technique. We shall discuss two classes of solutions over constant background: soliton-like solutions and quasi-rational solutions. Both classes have their analogues in the case of the Heisenberg ferromagnet equation related to the same Lie algebra.

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T. Valchev. 2024-03-27. A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions. https://arxiv.org/abs/2403.18165

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