Long Van Cao
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 [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.
Poznań
OWN
2010.09.13
2010.06.29
artykuł
application/pdf
eng
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