Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation

2019/08/04 by B.B. Kutum, Kutum, Bayan, Gulgassyl Nugmanova +7 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1908.01371

openalex publication_date 2019/08/04 · openalex created_date 2019/08/13 · openalex updated_date 2026/07/28

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.

Citations

• Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice
• An integrable semi-discrete Degasperis-Procesi equation
• Darboux transformations and exact soliton solutions of integrable coupled spin systems related with the Manakov system
• Integrable Motion of Curves, Spin Equation and Camassa-Holm Equation

Cited by

• Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions

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