  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.

Exactly Solvable and Integrable Systems