Integrable Motion of Curves, Spin Equation and Camassa-Holm Equation

Abstract

In the present paper, we investigate some geometrical properties of the Camass-Holm equation (CHE). We establish the geometrical equivalence between the CHE and the M-CIV equation using a link with the motion of curves. We also show that these two equations are gauge equivalent each to other.

arXiv comment12 pages

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Cited by in corpus (4)

• Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation
• Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions
• Zakharov-Ito equation and Generalized Heisenberg ferromagnet-type equation: equivalence and related geometric curve flows
• Generalized Heisenberg Ferromagnet type Equation and Modified Camassa-Holm Equation: Geometric Formulation, Soliton Solutions and Equivalence