Author(s)

M. S. Ismail, S. H. Alaseri

Department of Math, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia.

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.

Three Coupled Nonlinear Schrodinger Equations, Finite Difference Method, Time Splitting Method, Interaction of Solitons

Ismail, M. and Alaseri, S. (2016) Computational Methods for Three Coupled Nonlinear Schrödinger Equations. Applied Mathematics, 7, 2110-2131. doi: 10.4236/am.2016.717168.