Wobbling phenomena with logarithmic law nonlinear Schrödinger equations for incoherent spatial Gaussons

We apply the equivalence particle principle to several nonlinear Schrödinger equations (NLSEs) that model the propagation of a spatial beam with logarithmic law nonlinearity. Using this principle, expressions for acceleration, spatial frequency, spatial period and other variables for a spatial soliton can be derived from the solution of the homogenous NLSE with logarithmic law nonlinearity. These results agree well with numerical simulations of the perturbed NLSE. We show that if the expression of the acceleration is bounded this means the spatial soliton propagates with a swing effect.