TITLE:
Computational Methods for Three Coupled Nonlinear Schrödinger Equations
AUTHORS:
M. S. Ismail, S. H. Alaseri
KEYWORDS:
Three Coupled Nonlinear Schrodinger Equations, Finite Difference Method, Time Splitting Method, Interaction of Solitons
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.17,
November
15,
2016
ABSTRACT: In this work, we will derive numerical
schemes for solving 3-coupled nonlinear Schrödinger equations using finite
difference method and time splitting method combined with finite difference
method. The resulting schemes are highly accurate, unconditionally stable. We
use the exact single soliton solution and the conserved quantities to check the
accuracy and the efficiency of the proposed schemes. Also, we use these methods
to study the interaction dynamics of two solitons. It is found that both
elastic and inelastic collision can take place under suitable parametric
conditions. We have noticed that the inelastic collision of single solitons
occurs in two different manners: enhancement or suppression of the amplitude.