Amplification of nonautonomous solitons in the Bose-Einstein condensates and nonlinear optics

Two types of amplification of solitons during the interactions for a nonautonomous nonlinear Schrödinger model with the time- and space-dependent dispersion, nonlinearity, and external potentials have been investigated with the similarity transformations and Hirota bilinear method. Type 1 refers to the generation of the large central amplitudes with small wings for two collisional solitons, and Type 2 refers to the generation of the amplified peaks for the bound solitons. Both amplifications in our study could be applied to generate the solitons with large maximum amplitudes in such systems as those with the soliton managed by the Feshbach resonance in Bose-Einstein condensates and with the dispersion-managed soliton in nonlinear optics.