Oscillation of spatial solitons in a waveguide with a symmetrical refractive index profile

Dynamics of (1+1)D spatial solitons in a Kerr medium with atransversely symmetrical refractive index profile is investigated.Propagation of solitons is analysed theoretically by using aneffective-particle approach. Analytical results show that the solitonoscillates periodically with a variable acceleration. The expressionof oscillatory period is derived by introducing a concept of `averageacceleration'. Both acceleration and oscillatory period aredetermined by the parameters of the input soliton and the waveguide.Propagations of solitons are simulated numerically and good agreementis obtained between the theoretical and numerical results.