Violation of symmetry in the Ginzburg-Landau equation and emergence of the continuum of periodic solutions (Q2723276)

Transforming the classical Ginzburg-Landau equation \(\Delta v+\lambda v(1-|v|^2)= 0\) in the form \(\varphi+ \omega^2\varphi+ \varepsilon\varphi(1- (\omega^2+ \varepsilon)|\varphi|^2)= 0\), the authors study those values of the energy variables \((\xi_1,\xi_2)\) for which solutions emerge from the function \(\psi= \xi_1 e^{i\omega t}+ \xi_2e^{-i\omega t}\).