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

In this paper an analytic solution 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 with a cubic and fifth-order nonlinearity is presented. The solution is obtained from the nonlinear wave equation by using the method of unidirectional waves, and takes into account the wave reflected at the input of the medium. In particular, the solution obtained describes propagation of a femtosecond laser pulse with a Gaussian temporal profile in a nonlinear dispersive-free instantaneous-response medium considered in the approximation of a weak nonlinearity.