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Membrane solitons as solitary waves of nonlinear string dynamics

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 Schrödinger equation.