  The exact solvability problem of the nonlinear equations describing the U(1)
invariant membranes is studied and the general solution for the static membrane
in D=2N+1-dimensional Minkowski space-time, including M-theory case D=11, is
obtained. The time-dependent Jacobi elliptic function solution describing a
family of contracting tori is also found, together with the solution
corresponding to a spinning torus characterized by the presence of the critical
rotation frequency Omega=T^{1/3}/pi^{1/2} expressed via the membrane tension T.
