THE INTEGRABLE CONFIGURATION OF THE DISORDERED N=3 DISCRETE SELF-TRAPPING EQUATION

We consider the discrete self-trapping equation with three degrees of freedom containing disorder in the system parameters. Using SU(3) notations a system of eight real first-order ordinary differential equations is derived. For the integrable configuration, an open chain with a single anharmonicity placed at the central site, we can deduce from this system a second-order oscillator equation for the probability amplitude of the central site excitation. Using the corresponding anharmonic potential for a study of the oscillations of the central oscillator amplitude, the dynamics of the chain can be mapped on the disorder-nonlinearity-parameter plane. We discuss the localization properties of the excitation energy transfer on the trimer. The interplay between nonlinearity and disorder leads to some interesting effects such as suppression and amplification of localization.