Search for: [Abstract = "In this paper, using a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium derived in \[8\] 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."]
