STATIONARY SOLUTIONS AND SELF-TRAPPING IN DISCRETE QUADRATIC NONLINEAR-SYSTEMS

We consider the simplest equations describing coupled quadratic nonlin ear (chi((2))) systems, which each consists of a fundamental mode reso nantly interacting with its second harmonic. Such discrete equations a pply, e.g., to optics, where they can describe arrays of chi((2)) wave guides, and to Solid state physics, where they can describe nonlinear interface waves under the conditions of Fermi resonance of the adjacen t crystals. Focusing on the monomer and dimer we discuss their Hamilto nian structure and find all stationary solutions and their stability p roperties. in one limit the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, wh ich is integrable. We show how the stationary solutions to the two sys tems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system, when going away from the near integrable limit.