Localized excitations in discrete nonlinear Schrödinger systems: Effects of nonlocal dispersive interactions and noise

Abstract

A one-dimensional discrete nonlinear Schrödinger (DNLS) model with the power dependence, r − s on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exploited and the results of both approaches are compared. Both on-site and inter-site stationary states are investigated. It is shown that for s sufficiently large all features of the model are qualitatively the same as in the DNLS model with nearest-neighbor interaction. For s less than some critical value, s cr, there is an interval of bistability where two stable stationary states exist at each excitation number. The bistability of on-site solitons may occur for dipole-dipole dispersive interaction ( s = 3), while s cr for inter-site solitions is close to 2.1. In the framework of the DNLS equation with nearest-neighbor coupling we discuss the stability of highly localized, “breather-like”, excitations under the influence of thermal fluctuations. Numerical analysis shows that the lifetime of the breather is always finite and in a large parameter region inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping.