Solitons are localized, moving, nonlinear pulses of energy that are known to propagate without change in shape or amplitude in many lossless, nonlinear, uniform systems. In nonuniform systems, however, the soliton properties usually change as it travels through the nonuniformity. The proposed research is an analytical and numerical study of the characteristics of solitons in nonuniform systems. The purpose of the investigation is to explore how the nonuniformity of a nonlinear medium can be tailored to achieve certain desired modifications of the soliton such as reshaping, amplification, compression, or reflection. It is proposed to consider three different systems in which the nonuniformity is controllable: Solitons on nonuniform nonlinear transmission lines; solitons on axially-nonuniform optical fibers; and solitons in a nonuniform plasma bounded by a grid-plate structure. The results of the proposed investigation are expected to have a more general applicability, however, because the basic equations governing solitons in the three systems are identical in form to those in several other systems of current interest such as surface and internal water waves, acoustic waves in a crystal lattice, and magnetohydrodynamic waves in plasmas.
