Dinh Thuan Bui, Goldstein Piotr, Viet Hung Nguyen, Hoai Son Doan
ultrashort pulses, Kerr media, Generalized Nonlinear Schrödinger Equation, solitons
In this paper, using a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium derived in  we study in the specific case of Kerr media. An obtained ultrashort pulse propagation equation which is called Generalized Nonlinear Schrödinger Equation usually has a very complicated form and looking for its solutions is usually a “mission impossible”. Theoretical methods to solve this equation are effective only for some special cases. As an example we describe the method of a developed elliptic Jacobi function expansion. Several numerical methods of finding approximate solutions are simultaneously used. We focus mainly on the following methods: Split-Step, Runge-Kutta and Imaginary-time algorithms. Some numerical experiments are implemented for soliton propagation and interacting high order solitons. We consider also an interesting phenomenon: the collapse of solitons.