We apply equivalence particle principle to a higher order spatial Nonlinear Schrodinger Equation (NLSE) that models the propagation of a beam with higher order nonlinearity (X-(5)). Using this principle, expressions for acceleration, spatial frequency, spatial period and other variables for a spatial soliton can be derived from the solution of a dual power law (or parabolic law) homogenous Nonlinear Schrodinger Equation(NLSE). These results agree well with numerical simulations of the perturbed Nonlinear Schrodinger Equation. We show that if the expression of the acceleration is bounded this means the spatial soliton propagates with a swing effect. Taking one step further in this theoretical study, we investigate the swing effect through the use of numerical simulations.