Parametric disorder effects on a subcritical stationary bifurcation under nonlinear gradient term

Effects of harmonic modulation of the threshold of the bifurcation are investigated in the one-dimensional cubic-quintic Ginzburg–Landau equation with real coefficients. We analyze the effects of the nonlinear gradient term which is of same order as the quintic term in the Ginzburg–Landau equation. Above the threshold, the nonlinear part of equation solutions are determined by the Poincaré–Lindstedt expansion approach. We show that for small values of the coefficient of the nonlinear gradient term, the stationary nonlinear solution change, the slope of the Nusselt number increases, while the curvature decreases with increasing values of the modulation amplitude.