Chiral superconducting membranes

We develop the dynamics of the chiral superconducting membranes (with null current) in an alternative geometrical approach either making a Lagrangian description and a Hamiltonian point of view. Besides this, we show the equivalence of the resulting descriptions 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. We compare the results with recent works that appeared in the literature.