Integrable Flows of Curves/Surfaces, Generalized Heisenberg Ferromagnet Equation and Complex Coupled Dispersionless Equation

Abstract

In the present paper, we study the Myrzakulov-XIII (M-XIII) equation geometrically. From the geometric point of view, we establish a link of the M-XIII equation with the motion of space curves in the 3-dimensional space $R^3$. We also show that the complex coupled dispersionless (CCD) equation can be derived from the geometrical formalism such that their curve flows are formulated. Finally, the gauge equivalence between the M-XIII equation and the CCD equation is established.

arXiv comment13 pages

References in corpus (5)

• Complex short pulse and coupled complex short pulse equations
• Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials
• Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
• Integrability of the Gauss-Codazzi-Mainardi equation in 2+1 dimensions
• Darboux transformations and exact soliton solutions of integrable coupled spin systems related with the Manakov system

Cited by in corpus (3)

• Coupled Dispersionless and Generalized Heisenberg Ferromagnet Equations with Self-Consistent Sources: Geometry and Equivalence
• Dispersionless Limits of Some Integrable Equations
• Dispersionless Limits of Integrable Generalized Heisenberg Ferromagnet Equations