Periodic Nucleation Solutions of the Real Ginzburg-Landau equation in a Finite Box

In the vicinity of the threshold of a continuous pattern-forming instability a description of the basic periodic solution and its slow modulations is possible by perturbation theory [Newell & Whitehead, 1969; Segel, 1969; Stuart & Di Prima, 1978]. For quasi-one-dimensional, stationary, and periodic patterns formed from an unstructured state through a continuous soft-mode finite-q instability, a description in terms of A(x, t) satisfying the real Ginzburg–Landau equation is as follows