SMALL-AMPLITUDE SOLITARY WAVES ON A LATTICE SUBJECT TO NONVANISHING BOUNDARY-CONDITIONS

It is shown that the dynamics of small-amplitude pulses of the two commonly used discrete versions of the nonlinear Schrodinger equation can be described by the same lattice equation if the background amplitude is not close to unity. It allows us to use an analytical expression for a soliton of an integrable version obtained in the small-amplitude limit to generate solitary-wave solutions of the nonintegrable model. The existence of long-lived stable localized pulses against the nonzero background is discovered. It is found numerically that solitary pulses interact elastically with each other, i.e., they display all of the properties of solitons. In the case when the background amplitude is equal to unity, the integrable discrete model reduces to the Toda lattice.