On a zero curvature representation for bosonic strings and p-branes

It is shown that a zero curvature representation for D-dimensional p-brane equations of motion originates naturally in the geometric (Lund-Regge-Omnes) approach. To study the possibility to use this zero curvature representation for investigation of nonlinear equations of p-branes, the simplest case of D-dimensional string (p = 1) is considered. The connection is found between the SO(1,1) gauge (world-sheet Lorentz) invariance of the string theory with a nontrivial dependence on a spectral parameter of the Lax matrices associated with the nonlinear equations describing the embedding of a string world-sheet into flat D-dimensional space-time. Namely, the spectral parameter can be identified with a parameter of constant SO(1,1) gauge transformations, after the deformation of the Lax matrices has been performed.