Abstract
This paper is a theoretical study of solitons governed by the nonlinear Schrödinger's equation (NLSE) with non-Kerr law nonlinearity. The soliton perturbation theory is used to obtain the parameter dynamics of solitons that are governed by this equation. This study is extended to the case of the vector NLSE and its further generalization. In addition, we have studied the adiabatic parameter dynamics of solitons in presence of perturbation terms.