  In the present paper, we study the integrable 2-layer generalized Heisenberg
ferromagnet equation (HFE). The relation between this generalized HFE and
differential geometry of curves is established. Using this relation we found
the geometrical equivalent counterpart of the 2-layer spin system which is the
2-component KdV equation. Finally, the gauge equivalence between these
equations is established.

Exactly Solvable and Integrable Systems