On nonlocal reductions of a generalized Heisenberg ferromagnet equation

Tihomir Valchev, Ratbay Myrzakulov, Gulgassyl Nugmanova, Kuralay Yesmakhanova, Kuralay Yesmakhanova

2019

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DOI 10.1063/1.5127502
Data confidence 85 high
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Abstract

We study nonlocal reductions of a coupled system of equations in 1 + 1 dimensions of the Heisenberg ferromagnet type. The system under consideration is completely integrable through inverse scattering transform and has a Lax pair related to a linear bundle in pole gauge. We describe the integrable hierarchy of nonlinear equations related to our system in terms of generating operators. We present some special solutions associated with four distinct discrete eigenvalues of scattering operator. Using the Lax pair diagonalization method, we derive recurrence formulas for the conserved densities and find the first two simplest densities.