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

Autor: Mohamed M. Mousa, Praveen Agarwal, Fahad Alsharari, Shaher Momani
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-15 (2021)
Druh dokumentu: article
ISSN: 1687-1847
DOI: 10.1186/s13662-021-03505-7
Popis: Abstract 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 ) $(2+ 1)$ -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.
Databáze: Directory of Open Access Journals
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje