Open AccessGeometric Flows of Curves, Two-Component Camassa-Holm Equation and Generalized Heisenberg Ferromagnet Equation
Author(s) -
Gulgassyl Nugmanova,
Aigul Taishiyeva,
Ratbay Myrzakulov,
Tolkynai Myrzakul
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2090/1/012068
Subject(s) - integrable system , camassa–holm equation , mathematics , equivalence (formal languages) , component (thermodynamics) , mathematical analysis , integro differential equation , ferromagnetism , space (punctuation) , mathematical physics , riccati equation , physics , partial differential equation , pure mathematics , quantum mechanics , linguistics , philosophy
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.