Class of Nonlinearity Control Parameter for Bright Solitons of Non-Autonomous NLSE With Trapping Potential

We have obtained the family of exact soliton solutions, of the non-autonomous nonlinear Schrödinger equation with the harmonic trap, by invoking the isospectral deformation technique, which describe the propagation of bright solitons in the 1-D Bose-Einstein condensate confined by a harmonic potential with a varying-in-time longitudinal trapping frequency. This generalization also enables one to analytically study the effect of the nonlinearity control parameter in managing the amplitude and width of the soliton profile.