Conservative finite difference schemes for the chiral nonlinear Schrödinger equation

Boundary value problems

Ayhan Aydin¹  Mohammad S Ismail²  Khalil S Al-Basyouni² 

[1] Department of Mathematics, Atilim University, Ankara, Turkey;Department of Mathematics, College of Science, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: Soliton Solution;    Finite Difference Scheme;    Discrete Analog;    Dark Soliton;    Bright Soliton;   

DOI  :  10.1186/s13661-015-0350-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY