Propagation of an intense short laser pulse in nonuniform plasma

Propagation of an intense laser pulse in a cold electron-ion plasma is considered. Starting with the fully relativistic equations, for pancake-shaped pulses, a one-dimensional nonlinear Schrodinger equation is derived. It is shown, in quasi-stationary stage, both localized and cusp solution exist and relativistic effects cause solitons to move slower as their amplitude increases. These observations indicate particle-like behavior for localized solutions.