  Among solutions of n-Gelfand-Dikii's hierarchy there exists a remarkable
solution W, which satisfies the string equation. We call it Witten's solution
because according to the Witten conjecture the function F(x_1, x_2, x_3,...) =
W(x_1,(x_2)/2, (x_3)/3,...) is the generating function for intersection nambers
of Mumford-Morita-Muller cohomological classes of the moduli space of n-spin
Riemann surfaces. This conjecture was proved by Kontsevich for n=2 and by
Witten himself for surfaces of genus 0.
  In this paper we find recurrence relations between coefficients of Taylor
series of W. This reduces the Witten's conjecture to conjecture that the
Mamford-Morita-Muller numbers satisfy to the same relations. These relations
give also an algorithm for calculation of $n$-spin Mamford-Morita-Muller
numbers in assuming that the Witten conjecture is true. Moreover we prove that
F(x_1,x_2,...,x_{n-1},0,0,...)= W(x_1, (x_2)/2,...,(x_{n-1})/(n-1),0,0,...).
