On neutrino oscillations in nonuniform matter

An approximate analytical solution of equations of neutrino oscillations is obtained for the case of small vacuum mixing angles in matter with an arbitrarily varying density. Oscillations in matter with a periodically varying density are also considered in two cases: for a sinusoidal density variation and for a periodic step function. In the first case use is made of the earlier obtained approximate solution and in the second, an exact solution is found. It is shown that under certain conditions a parametric amplification of neutrino oscillations may take place, which is analogous to a parametric resonance is mechanics and electromagnetism. 10 refs