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

Guldana Bekova; Kuralay Yesmakhanova; Gaukhar Shaikhova; Gulgassyl Nugmanova; Ratbay Myrzakulov

paper

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

arXiv:1812.02152

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.

13 pages