Ismail, M.S., Al-Basyouni, K.S. and Aydin, A. (2015) Conservative Finite Difference Schemes for the Chiral Nonlinear Schrödinger Equation. Boundary Value Problem, 2015, 89.
http://dx.doi.org/10.1186/s13661-015-0350-4

has been cited by the following article:

• 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.