On the reflection of solitons of the cubic nonlinear Schrödinger equation

Theodoros Katsaounis; Dimitrios Mitsotakis

doi:10.1002/mma.4070

On the reflection of solitons of the cubic nonlinear Schrödinger equation

Theodoros Katsaounis, Dimitrios Mitsotakis

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1013-1018
Number of pages	6
Journal	Mathematical Methods in the Applied Sciences
Volume	41
Issue number	3
DOIs	https://doi.org/10.1002/mma.4070
State	Published - Jul 5 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Victoria University of Wellington[208964]

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https://repository.kaust.edu.sa/bitstream/10754/619215/1/km2.pdf

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title = "On the reflection of solitons of the cubic nonlinear Schr{\"o}dinger equation",

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 Schr{\"o}dinger 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.",

author = "Theodoros Katsaounis and Dimitrios Mitsotakis",

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AU - Mitsotakis, Dimitrios

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PY - 2016/7/5

Y1 - 2016/7/5

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/619215

UR - https://arxiv.org/abs/1602.04424

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On the reflection of solitons of the cubic nonlinear Schrödinger equation

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