Nonlocal Reductions of a Generalized Heisenberg Ferromagnet Equation

TL;DR

This paper investigates nonlocal reductions of integrable coupled equations of the Heisenberg ferromagnet type, deriving hierarchies, special solutions, and conserved densities using Lax pair methods.

Contribution

It introduces new nonlocal reductions of Heisenberg ferromagnet equations and develops methods to analyze their integrable hierarchies and conserved quantities.

Findings

Derived recurrence formulas for conserved densities.

Presented special solutions with four discrete eigenvalues.

Established the integrable hierarchy related to the system.

Abstract

We study nonlocal reductions of coupled equations in $1+1$ dimensions of the Heisenberg ferromagnet type. The equations under consideration are completely integrable and have 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 the scattering operator. Using Lax pair diagonalization method, we derive recurrence formulas for the conserved densities and find the first two simplest conserved densities.