Abstract
By taking values in a commutative subalgebra gln,C, we construct a new generalized Zn-Heisenberg ferromagnet model in (1+1)-dimensions. The corresponding geometrical equivalence between the generalized Zn-Heisenberg ferromagnet model and Zn-mixed derivative nonlinear Schrödinger equation has been investigated. The Lax pairs associated with the generalized systems have been derived. In addition, we construct the generalized Zn-inhomogeneous Heisenberg ferromagnet model and Zn-Ishimori equation in (2+1)-dimensions. We also discuss the integrable properties of the multi-component systems. Meanwhile, the generalized Zn-nonlinear Schrödinger equation, Zn-Davey–Stewartson equation and their Lax representation have been well studied.
Highlights
Advances in Mathematical Physics2. -Heisenberg Ferromagnet Model e Heisenberg ferromagnet (HF) model in (1+1)-dimensions [4] is an important integrable equation which reads as
Introduction e Heisenberg ferromagnet (HF) model is one of the most investigated integrable systems which plays an important role in the two-dimensional (2D) gravity theory [1] and anti-de Sitter/conformal field theories [2, 3]
It is proved that the HF model is gauge and geometric equivalent to the nonlinear Schrödinger (NLS) equation [4, 5]. (1+1)-dimensional generalized HF models involving inhomogeneous and higher order deformed HF models have been analyzed [6, 7]. e deformed HF models in (2+1)-dimensions have been investigated, such as the higher order HF models [8, 9], the HF models with self-consistent potentials [10], the Ishimori equation [11], and inhomogeneous HF models [12, 13]
Summary
2. -Heisenberg Ferromagnet Model e Heisenberg ferromagnet (HF) model in (1+1)-dimensions [4] is an important integrable equation which reads as. Where S denotes the constraint S2 = 1. Where 푆 = ∑3푖=1푆푖휎푖, 푆2 = 퐼, 푡푟푆 = 0 and 휎 (푖 = 1, 2, 3) are Pauli matrices
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