期刊名称：Computational Methods in Science and Technology
印刷版ISSN：1505-0602
出版年度：2010
卷号：16
期号：Special 2
出版社：Poznan Supercomputing and Networking Center
摘要：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 NonlinearSchr.dinger Equation usually has a very complicated form and looking for its solutions is usually a "mission impossible". Theoreticalmethods 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 thefollowing methods: Split-Step, Runge-Kutta and Imaginary-time algorithms. Some numerical experiments are implemented for solitonpropagation and interacting high order solitons. We consider also an interesting phenomenon: the collapse of solitons
