Stability of multiple pulses in discrete systems - art. no. 036604

The stability of multiple-pulse solutions to the discrete nonlinear Schrodi nger equation is considered. A bound state of widely separated single pulse s is rigorously shown to be unstable, unless the phase shift Delta phi betw een adjacent pulses satisfies Delta phi = pi. This instability is accounted for by positive real eigenvalues in the linearized system. The analysis le ading to the instability result does not, however, determine the linear sta bility of those multiple pulses for which Delta phi = pi between adjacent p ulses. A direct variational approach for a two-pulse predicts that it is li nearly stable if Delta phi = pi, and if the separation between the individu al pulses satisfies a certain condition. The variational approach can easil y be generalized to study the stability of N pulses for any N greater than or equal to 3. The analysis is supplemented with a detailed numerical stabi lity analysis.