Analytic solution of the wave equation describing dispersion-free propagation of a femtosecond laser pulse in a medium with a cubic nonlinearity

An analytic solution is obtained of the wave equation describing the propagation of a femtosecond laser pulse with a Gaussian temporal profile in a nonlinear dispersion-free instant-response medium, considered in the approximation of a weak nonlinearity and taking account of the wave reflected at the input.