Integrability and structural stability of solutions to the Ginzburg–Landau equation

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Abstract
The integrability of the Ginzburg–Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painlevé property, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schrödinger (NLS) equation. Regarding the Ginzburg–Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two‐tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10−6).

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