Slow time-periodic solutions of cubic-quintic Ginzburg-Landau equation. II: Heteroclinic orbits
[For part I see ibid. No. 4, 403-415 (1998; Zbl 0969.35013).] The equation (a Ginzburg-Landau equation) \[ W_t= c_0W+(c_0+ i\varepsilon c_1) W_{xx}- ((c_0/2)+ i\varepsilon c_2)|W|^2W- ((c_0/2)+ i\varepsilon c_3)|W|^4 W \] is considered; \((x,t)\in \mathbb{R}\times \mathbb{R}\), \(W(x,t)\) is a complex function, \(c_k\), \(k= 0,\dots 3\), are real constants, and \(\varepsilon\) is a small parameter. The existence of periodic solutions of the form \(W(x,t)= \rho(x) e^{i(\theta(x)- \varepsilon\omega t)}\), is studied. There are given also numerical solutions for some values of \(\varepsilon\).
scientific article; zbMATH DE number 1553650