PHONON SCATTERING BY BREATHERS IN THE DISCRETE NONLINEAR SCHRÖDINGER CHAIN

Linear theory for phonon scattering by discrete breathers in the discrete nonlinear Schrödinger equation using the transfer matrix approach is presented. Transmission and reflection coefficients are obtained as a function of the wave vector of the input phonon. The occurrence of a nonzero transmission, which in fact becomes perfect for a symmetric breather, is shown to be connected with localized eigenmodes thresholds. In the weak-coupling limit, the perfect reflection is shown to exist, which requires two scattering channels. A necessary condition for a system to have a perfect reflection is also considered in a general context.