  The phase transitions in a realistic system with triplet pairing, dense
neutron matter, have been investigated. The spectrum of phases of the
$^3P_2-^3F_2$ model, which adequately describes pairing in this system, is
analytically constructed with the aid of a separation method for solving BCS
gap equation in states of arbitrary angular momentum. In addition to solutions
involving a single value of the magnetic quantum number (and its negative),
there exist ten real multicomponent solutions. Five of the corresponding
angle-dependent order parameters have nodes, and five do not. In contrast to
the case of superfluid $^3$He, transitions occur between phases with nodeless
order parameters. The temperature dependence of the competition between the
various phases is studied.
