Discrete lattice effects on breathers in a spatially linear potential

In the presence of a spatially linear, time dependent potential, we study discrete lattice effects on a nonlinear Schrödinger breather in the form of a composite excitation comprising two soliton components. We obtain an exact breather solution by generalizing the Hirota method to include the external potential. The solution is a discrete generalization of the two-soliton continuum solution with the initial condition as a superposition of two identitcal solitons. Unlike the continuum breather in the presence of a static ramp, the discrete breather will break up into two spatially separate, coherent structures undergoing bounded individual motions. We show that this breakup is a general discrete effect for breathers in an external potential.