  We develop the dynamics of the chiral superconducting membranes(with null
current) in an alternative geometrical approach. Besides of this, we show the
equivalence of the resulting description to the one known Dirac-Nambu-Goto
(DNG) case. Integrability for chiral string model is obtained using a proposed
light-cone gauge. In a similar way, domain walls are integrated by means of a
simple ansatz.
