Defect-induced spatial coherence in the discrete nonlinear Schrödinger equation.
We have considered the discrete nonlinear Schrödinger equation (DNLSE) with periodic boundary conditions in the context of coupled Kerr waveguides. The presence of a defect in the central oscillator equation can induce quasiperiodic or large chaotic amplitude oscillations. As for the quasiperiodic dynamics, an enhancement of the amplitude correlations in certain oscillator pairs can take place. However, when the array dynamics becomes chaotic, these correlations are destroyed, and, for suitable defects, synchronization, in the information sense, of certain signals arises in this Hamiltonian system. A numerical continuation analysis clarifies the onset of this dynamical regime. In this case, phase synchronization follows with a peculiar distribution of the Liapunov exponents. These effects occur for initial conditions in a small neighborhood of a family of stationary solutions. We have also found a regime characterized by persistent localized chaotic amplitudes. We have generalized these results to take into account birefringent effects in waveguides.
Pando
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CL
IFUAP, Universidad Autónoma de Puebla, Apartado Postal J-48. Puebla, Puebla 72570, Mexico.
Doedel
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EJ
D015233:Models, Statistical; D008962:Models, Theoretical; D009068:Movement; D017711:Nonlinear Dynamics; D009991:Oscillometry; D055585:Physical Phenomena; D010825:Physics