English

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}
}

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11 pages