Adiabatic matter effect with three generation neutrinos and the solar neutrino problem

We find an exact analytic solution for the time evolution of a three Dirac neutrino system adiabatically oscillating in matter, constructing explicitly the relevant $3\times 3$ mixing matrix in matter. Using this result we investigate the solar neutrino data in a scenario where the neutrino masses are such that $m_1\alt m_2\ll m_3$, taking into account several phenomenological constraints on neutrino mixing angles and masses. A solution of the solar neutrino problem for large values of the parameter $\delta m^2=m_2^2-m_1^2$ which are not usually associated with a resonance is found. This is an essentially three-generation effect.