Nature of transitions in augmented discrete nonlinear Schrodinger equations

We investigate the nature of the transitions between free and self-trapping states occurring in systems described by augmented forms of the discrete n onlinear Schrodinger; equation. These arise from an interaction between a m oving quasiparticle (such as an electron or an exciton) and lattice vibrati ons. when the effects of nonlinearities in interaction potential and restor ing force are included. We derive analytic conditions for the stability of the free state and the crossover between first- and second-order transition s. We demonstrate our results for different types of nonlinearities in the interaction potential and restoring force. We find that, depending on the t ype of nonlinearity, it is possible to have both first- and second-order tr ansitions. We discuss possible hysteresis effects. [S1063-651X(99)13305-1].