On the reflection of solitons of the cubic nonlinear Schrödinger equation. (5th July 2016)

• Record Type: Journal Article
• Authors: Katsaounis, Theodoros; Mitsotakis, Dimitrios
• Other Names: Barbatis Gerassimos guestEditor.; Dougalis Vassilios guestEditor.; Stratis Ioannis G. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 3(2018)
• Page Start: 1013
• Page End: 1018
• Publication Date: 2016-07-05
• Subjects: nonlinear Schrödinger equation -- relaxation method -- soliton reflection -- dark and bright solitons; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4070
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit–explicit type Crank–Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall. Copyright © 2016 John Wiley & Sons, Ltd.