TITLE: Randomness effects on modulational instability of Davydov's model
             and multiscale analysis of the long wave short wave resonances

                   Department of Theoretical Physics, 
                   National Institute for Physics and Nuclear Engineering
                   Bucharest, POB MG-6, 76900, Romania

ABSTRACT:
 

The modulational instability of Davydov's model is discussed from the statistical point of view considering the amplitude of the amide I oscillator as a random variable. The linear stability of the discrete Wigner-Moyal transform of the kinetic equation for the two point correlation function is studied. Both a gaussian and a lorentzian form for teh initial unperturbed wave spectrum are discussed. Also a multiscale analysis of Davydov's model in the long-wave short-wave resonance condition is performed and Zakharov -Benney equation are obtained for the dominant amplitude. The modulational instability of ZB eq. is compared with the results of the previous discussion of the discrete Davydov equations.

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