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The concept of nonautonomous soliton dispersion management pertaining to the propagation of chirped nonautonomous Raman colored solitons through a dispersion oscillating fiber in the presence of an electrooptic phase modulator and also by taking into consideration the effect due to self-induced Raman scattering on the propagation of optical solitons when the soliton amplitude does not vary significantly during self-scattering, has been studied. The amplitudes and speeds of these nonautonomous solitons, during the propagation and after the interaction are no longer found to be the same as those prior to the interaction. Moreover, intense soliton pulse amplification has been obtained, which forms the main results of this paper. In the context of Bose-Einstein condensates, the aforementioned scenario has also been interpreted as the dynamics of the condensates with linear and quadratic external potentials in an optical trap.

The concept of soliton dispersion management pertaining to the effect of varying dispersion with external harmonic oscillator potential for chirped solitons have been studied in detail with emphasis on the various aspects of dispersion management of solitons. The interaction scenarios pertaining to in-phase- and off-phase injection with equal and unequal amplitudes are dealt elaborately. Suppression of interaction forces between the dispersion managed solitons, optical soliton pulse amplification and robustness of bound soliton states to collisions, are some of the main results of this article.

The possibility of nonlinear pairing of bright and dark optical solitons at the wave phase cross modulation in a nonlinear dispersive medium is shown. The realization of fundamentally novel methods for the stabilization of powerful wave packets in the positive and negative group velocity dispersion regions of the interacting waves with different colors is demonstrated. The dynamics of coupling dark and bright optical solitons in frames of a system of two bound nonlinear Schrodinger equations are investigated analytically and numerically. The role of disturbing factors, linear absorption, duration, pulse position, and nonlinearity mismatch are discussed. The influence of the stimulated Raman self-scattering effect and modulation instability on the dynamics of bright and dark soliton pairing is investigated. The process of soliton collision is studied. >