Abstract

Families of solutions to the field equations of the covariant BRST invariant effective action of membrane theory are constructed. The equations are discussed in a double-dimensional reduction; they lead to a nonlinear equation for a one-dimensional extended object. One family of solutions of these equations are solitary waves with several properties of solitonic solutions in integrable systems, providing evidence that in this double-dimensional reduction the nonlinear equations are an integrable system. The other family of solutions found exploits the property that the nonlinear system under some assumptions is equivalent to a nonlinear Schrodinger equation.