SOLITON DYNAMICS IN THE DISCRETE NONLINEAR SCHRODINGER-EQUATION

Using a variational technique, based on an effective Lagrangian, we an alyze static and dynamical properties of solitons in the one-dimension al discrete nonlinear Schrodinger equation with a homogeneous power no nlinearity of degree 2 sigma + 1. We obtain the following results. (i) For sigma < 2 there is no threshold for the excitation of a soliton; solitons of arbitrary positive energies, W = Sigma\u(n)\(2), exist. (i i) Range of multistability: there is a critical value of sigma, sigma( cr) approximate to 1.32, such that for sigma(cr) < sigma < 2, there ex ist three soliton-like states in a certain finite intermediate range o f energies, two stable and one unstable (while there is no multistable regime in the continuum NLS equation). For energies below and above t his range, there is a unique soliton state which is stable. (iii) For sigma greater than or equal to 2, there exists an energy threshold for formation of the soliton. For all sigma > 2 there exist two soliton s tates, one narrow and one broad. The narrow soliton is stable, while t he broad one is not. (iv) We find an energy criterion for the excitati on of solitons by initial configurations which are narrowly concentrat ed in few lattice sites.