  We present the complete solution to a 95% scalar field cosmological model in
which the dark matter is modeled by a scalar field $\Phi$ with the scalar
potential $V(\Phi)=V_{o}[ \cosh {(\lambda \sqrt{\kappa_{o}}\Phi)}-1]$ and the
dark energy is modeled by a scalar field $\Psi$, endowed with the scalar
potential $\tilde{V}(\Psi)=\tilde{V_{o}}[ \sinh {(\alpha
\sqrt{\kappa_{o}}\Psi)}] ^{\beta}$. This model has only two free parameters,
$\lambda$ and the equation of state $\omega_{\Psi}$. With these potentials, the
fine tuning and the cosmic coincidence problems are ameliorated for both dark
matter and dark energy and the models agrees with astronomical observations.
For the scalar dark matter, we clarify the meaning of a scalar Jeans lenght and
then the model predicts a suppression of the Mass Power Spectrum for small
scales having a wave number $k > k_{min,\Phi}$, where $k_{min,\Phi} \simeq 4.5
h {\rm Mpc}^{-1}$ for $\lambda \simeq 20.28$. This last fact could help to
explain the dearth of dwarf galaxies and the smoothness of galaxy core halos.
  From this, all parameters of the scalar dark matter potential are completely
determined. The dark matter consists of an ultra-light particle, whose mass is
$m_{\Phi} \simeq 1.1\times 10^{-23} {\rm eV}$ and all the success of the
standard cold dark matter model is recovered. This implies that a scalar field
could also be a good candidate as the dark matter of the Universe.
