Conservative finite difference schemes for the chiral nonlinear Schrödinger equation

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Date
2015-08-08
Authors
ISMAIL, Mohammed S.
AL-BASYOUNI, Khalil S.
AYDIN, Ayhan
Journal Title
Journal ISSN
Volume Title
Publisher
Boundary Value Problems
Abstract
In this paper, we derive three finite difference schemes for the chiral nonlinear Schrödinger equation (CNLS). The CNLS equation has two kinds of progressive wave solutions: bright and dark soliton. The proposed methods are implicit, unconditionally stable and of second order in space and time directions. The exact solutions and the conserved quantities are used to assess the efficiency of these methods. Numerical simulations of single bright and dark solitons are given. The interactions of two bright solitons are also displayed.
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Keywords
mathematics
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