THE NONLINEAR SCHRÖDINGER EQUATION FOR THE DELTA-COMB POTENTIAL: QUASI-CLASSICAL CHAOS AND BIFURCATIONS OF PERIODIC STATIONARY SOLUTIONS

摘要: The nonlinear Schrodinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb time-independent can be solved analytically in terms Jacobi elliptic functions and thus provides useful insight into features stationary states Phenomena well-known from classical chaos are found, such as bifurcation transition to spatial chaos. relation new Bloch bands, looped period doubled analyzed detail. An analytic expression critical nonlinearity emergence bands derived. results generalized more realistic potential consisting peaks dynamical stability solutions comb discussed.