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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 scattering operator. Using the Lax pair diagonalization method, we derive recurrence formulas for the conserved densities and find the first two simplest conserved densities.
We present in this report 1+1 dimensional nonlinear partial differential equation integrable through inverse scattering transform. The integrable system under consideration is a pseudo-Hermitian reduction of a matrix generalization of classical 1+1 d
This paper is a continuation of our previous work in which we studied a sl(3) Zakharov-Shabat type auxiliary linear problem with reductions of Mikhailov type and the integrable hierarchy of nonlinear evolution equations associated with it. Now, we sh
In this paper, we study the generalized Heisenberg ferromagnet equation, namely, the M-CVI equation. This equation is integrable. The integrable motion of the space curves induced by the M-CVI equation is presented. Using this result, the Lakshmanan
We consider an auxiliary spectral problem originally introduced by Gerdjikov, Mikhailov and Valchev (GMV system) and its modification called pseudo-Hermitian reduction which is extensively studied here for the first time. We describe the integrable h
In this paper, we provide the geometric formulation to the two-component Camassa-Holm equation (2-mCHE). We also study the relation between the 2-mCHE and the M-CV equation. We have shown that these equations arise from the invariant space curve flow