Geometric Flows of Curves, Two-Component Camassa-Holm Equation and Generalized Heisenberg Ferromagnet Equation
Aigul Taishiyeva, Tolkynay Myrzakul, Gulgassyl Nugmanova, Shynaray, Myrzakul, Kuralay Yesmakhanova, Ratbay Myrzakulov
TL;DR
This paper explores the integrability and geometric interpretation of the M-CVI equation, establishing its equivalence with the two-component Camassa-Holm equation through gauge transformations and curve motion analysis.
Contribution
It introduces the M-CVI equation as an integrable model and demonstrates its geometric and gauge equivalence to the two-component Camassa-Holm equation.
Findings
The M-CVI equation is integrable.
The motion of space curves induced by the M-CVI equation is characterized.
The M-CVI and two-component Camassa-Holm equations are gauge equivalent.
Abstract
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 (geometrical) equivalence between the M-CVI equation and the two-component Camassa-Holm equation is established. Note that these equations are gauge equivalent each to other.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Topics in Algebra