TITLE:
Method of Lines for the Chiral Nonlinear Schrödinger Equation
AUTHORS:
K. S. AL-Basyouni, M. S. Ismail
KEYWORDS:
Method of Lines, Linear Multistep Method, Chiral Soliton, Interaction of Two Solitons
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.6,
June
3,
2020
ABSTRACT: In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically. Two numerical methods are derived using the explicit Runge-Kutta method of order four and the linear multistep method (Predictor-Corrector method of fourth order). The resulting schemes of fourth order accuracy in spatial and temporal directions. The CNSE is non-integrable and has two kinds of soliton solutions: bright and dark soliton. The exact solutions and the conserved quantities of CNSE are used to display the efficiency and robustness of the numerical methods we derived. Interaction of two bright solitons for different parameters is also displayed.