A (2+1)-dimensional integrable spin model(the M-XXII equation) and Differential geometry of curves/surfaces

TL;DR

This paper explores a (2+1)-dimensional integrable spin model, the M-XXII equation, by linking it to differential geometry of curves and surfaces, revealing geometric insights into its integrability.

Contribution

It establishes a Lakshmanan equivalent of the M-XXII equation through differential geometry, providing a novel geometric perspective on this integrable spin model.

Findings

Identified the geometric structure underlying the M-XXII equation

Established a Lakshmanan equivalence with a geometric interpretation

Enhanced understanding of integrability via differential geometry

Abstract

Using the differential geometry of curves and surfaces the Lakshmanan equivalent counterpart of the M-XXII equation is found ... .