We investigate the nature of the transitions between free and self-trapping states occurring in systems described by augmented forms of the discrete nonlinear Schrödinger equation. These arise from an interaction between a moving quasiparticle (such as an electron or an exciton) and lattice vibrations, when the effects of nonlinearities in interaction potential and restoring force are included. We derive analytic conditions for the stability of the free state and the crossover between first- and second-order transitions. We demonstrate our results for different types of nonlinearities in the interaction potential and restoring force. We find that, depending on the type of nonlinearity, it is possible to have both first- and second-order transitions. We discuss possible hysteresis effects.

• Received 15 December 1998

DOI:https://doi.org/10.1103/PhysRevE.59.6306