  We show that to describe properly the low energy excitations of $CuGeO_{3}$
one must include the effects of a transverse antiferromagnetic coupling, which
is estimated to be $J_{\perp}=0.15 J$. Owing to this coupling the frustration
in the chains is significantly lower than recent 1D estimates based on purely
one-dimensional arguments, we find $J_{2}=0.2 J$. Furthermore we have found a
strong modulation of the nearest neighbour coupling due to the static
distortion $\delta = 0.065$, which is 5 times higher than that previously
deduced from a 1D chain approach. Our set of parameters gives, i) a value of
the distorsion which agreeswell with some recent estimate for a lower bound, we
are able to perfectly reproduce ii)the dispersions, iii) the experimental
susceptibility at both high and low temperatures. By performing DMRG
calculations for 2 coupled chains we have analysed the effect of the transverse
coupling on the ratio of singlet to triplet gaps. The ratio is very sensitive
to the parameters and the universality reported in the strict one dimensional
case is lost. As an additional point, we provide a simple picture to explain
the interesting new feature observed in recent inelastic neutron scattering
experiments: the existence of a second branch of excitations.
