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Families of solutions to the field equations of the covariant BRST invarianteffective action of the membrane theory are constructed. The equations arediscussed in a double dimensional reduction, they lead to a nonlinear equationfor a one dimensional extended object. One family of solutions of theseequations are solitary waves with several properties of solitonic solutions inintegrable systems, giving evidence that in this double dimensional reductionthe nonlinear equations are an integrable system. The other family of solutionsfound, exploits the property that the non linear system under some assumptionsis equivalent to a non linear Schr$\ddot {o}$dinger equation.Comment: 15 pages, latex=2

Membrane solitons as solitary waves of nonlinear string dynamics