Characteristic features of the dynamics of the Ginzburg-Landau equation in a plane domain (Q5941944)

The authors studied the boundary value problem \(w_t=k_0 \Delta w+k_1w-k_2 w|w|^2\), \(w|_{\partial \Omega_0}=0\) in the domain \(\Omega_0= \{(x,y):0\leq x\leq l_1\), \(0\leq y\leq l_2\}\). Here \(w\) is a complex-valued function and \(k_j\), \(j=0,1,2\), are complex constants with \(\text{Re} k_j>0\). The authors showed that under a rather general choice of the parameters \(l_1\) and \(l_2\), the number of stable invariant tori in the problem, as well as their dimensions, grows infinitely as \(\text{Re} k_j\to 0\), \(j=0,1\).