Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential

We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schrödinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly distributed. Such solutions exist in certain constraint conditions on the coefficients depicting dispersion, nonlinearity, and gain (loss). Various shapes of bright solitons and interesting interactions between two solitons are observed. Physical applications of interest to the field and stability of the solitons are discussed.