Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation
Exactly Solvable and Integrable Systems
2019-08-06 v1
Abstract
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 flows in three-dimensional Euclidean geometry. Using this approach we have established the geometrical equivalence between the 2-mCHE and the M-CV equation. The gauge equivalence between these equations is also considered.
Keywords
Cite
@article{arxiv.1908.01371,
title = {Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation},
author = {Bayan Kutum and Gulgassyl Nugmanova and Tolkynay Myrzakul and Kuralay Yesmakhanova and Ratbay Myrzakulov},
journal= {arXiv preprint arXiv:1908.01371},
year = {2019}
}
Comments
11 pages