The one-particle type temporal soliton exists by maintaining a balance between dispersive linear contributions on the one hand and non-linear effects on the other. The linear contributions occur from processes such as group velocity and polarization mode dispersion. The nonlinear features occur from Kerr, or power law non-Kerr behavior. In addition, a variety of perturbations, such as damping, Brillouin scattering, and Raman effects exist to alter the simple soliton solution. In this paper, we review the propagation of temporal solitons in power law non-Kerr media. This is developed through the higher nonlinear Schroedinger's equation (HNLSE). Also, the fundamentals of multiple-scales are presented that will be used to yield quasi-stationary solitons when perturbations are present. In waveguides, the one-particle type spatial soliton exists by maintaining a balance between the linear propagational diffraction and non-linear self-focusing, while possibly being subjected to a variety of perturbations. Here, we use a spatial optical soliton solution to the nonlinear Schroedinger equation in an inhomogeneous triangular refractive index profile as a small index perturbation to illustrate the oscillation property within a two dimensional waveguide. We determine, from the motion of spatial soliton, its effective acceleration, period of oscillation, and compare results with the Gaussian refractive index profile. Such spatial solitons behave as point masses existing in a Newtonian gravitational potential hole.