Capturing of solitons collisions and reflections in nonlinear Schrödinger type equations by a conservative scheme based on MOL

Advances in Difference Equations

article

Mousa, Mohamed M.¹  Agarwal, Praveen³  Alsharari, Fahad¹  Momani, Shaher⁶ 

[1] Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University;Department of Basic Engineering Sciences, Faculty of Engineering at Benha, Benha University;Department of Mathematics, Anand International College of Engineering;Department of Mathematics, Harish-Chandra Research Institute;International Center for Basic and Applied Sciences;Nonlinear Dynamics Research Center (NDRC), Ajman University, United Arab Emirates;Department of Mathematics, Faculty of Science, University of Jordan

关键词: Coupled nonlinear Schrödinger equation;    Nonlinear Schrödinger equation;    Method of lines;    Soliton collision;    Soliton reflection;   

DOI  :  10.1186/s13662-021-03505-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this work, we develop an efficient numerical scheme based on the method of lines (MOL) to investigate the interesting phenomenon of collisions and reflections of optical solitons. The established scheme is of second order in space and of fourth order in time with an explicit nature. We deduce stability restrictions using the von Neumann stability analysis. We consider a$(2+ 1)$ -dimensional system of a coupled nonlinear Schrödinger equation as a general model of nonlinear Schrödinger-type equations. We consider several numerical experiments to demonstrate the robustness of the scheme in capturing many scenarios of collisions and reflections of the optical solitons related to nonlinear Schrödinger-type equations. We verify the scheme accuracy through computing the conserved invariants and comparing the present results with some existing ones in the literature.

【 授权许可】

CC BY