Abstract
We develop a novel approach for treating in a unified manner the problem of N-neutrino oscillations in matter with density that varies in an arbitrary way along a neutrino's path. It is shown that the class of density functions, permitting exact analytic solutions for the two-flavor survival probability, can be considerably enlarged. For three flavors, we propose a general analytic scheme for calculating the non-adiabatic evolution of a neutrino state near the resonances.
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