Integrable Motion of Curves, Spin Equation and Camassa-Holm Equation
Assem Mussatayeva, Tolkynay Myrzakul, Gulgassyl Nugmanova, Kuralay, Yesmakhanova, Ratbay Myrzakulov
TL;DR
This paper explores the geometric relationships between the Camassa-Holm equation and related equations, revealing their equivalence through curve motion and gauge transformations, thus providing new insights into their integrable structures.
Contribution
It establishes the geometric and gauge equivalence between the Camassa-Holm equation and the M-CIV equation via curve motion analysis.
Findings
Camassa-Holm equation is geometrically equivalent to the M-CIV equation.
The two equations are gauge equivalent.
Geometric properties of the Camassa-Holm equation are elucidated.
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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Numerical methods for differential equations