Breakdown of the Phase Dynamics

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Abstract
We study the Ginzburg-Landau equations and the corresponding phase equations to investigate the wavelength changing process through the Eckhaus instability and the transition from a phase turbulence to an amplitude turbulence. A large deformation of amplitude is necessary for the transitions and so the phase description expressing slow modulation is broken down. We show by some numerical simulations what takes place in the phase equations at the transitions.

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