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

2024/03/27 by Valchev, T.
#17B80 #35C05 #35C08 #37K10 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2403.18165

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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