We use the reductive perturbation method to discuss the phase transition of the nonequilibrium superconductors induced by the injection of quasiparticles in the vicinity of the instability point Nqp~Nt. We solve the third order equation which is analogous to the time dependent Ginzburg-Landau equation exactly. We also discuss the behavior of various modes in the non-linear region for different N1 and temperature ranges. When the quasiparticle-phonon reaction is small,3/2Nc>Nt>Ne, we found that modes with wave number │q-qm│<k0. and Nqp<Nt, or modes with wave number │q-qm│<k0 are damped, stable or unstable according to whether the initial disturbance So are less, equal to or greater than the critical disturbance Sc.