  Families of solutions to the field equations of the covariant BRST invariant
effective action of the 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, giving 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 non linear system under some assumptions
is equivalent to a non linear Schr$\ddot {o}$dinger equation.
