Bright and dark solitons of the generalized nonlinear Schrödinger’s equation

This paper studies the generalized form of the nonlinear Schrödinger’s equation. The special cases of Kerr law, power law, parabolic law and the dual-power laws are considered. The 1-soliton solution is obtained in all of these four cases. The adiabatic parameter dynamics of the solitons due to perturbation terms are laid down. In addition, the analysis of dark soliton is also carried out. Finally, a few numerical simulations of these equations are given.