On a study of symmetries and conservation laws of a class of time fractional Schrödinger equations with nonlocal nonlinearities

Q. Hussain; F. D. Zaman; A. H. Bokhari; A. H. Kara

doi:10.1016/j.ijleo.2020.165619

On a study of symmetries and conservation laws of a class of time fractional Schrödinger equations with nonlocal nonlinearities

Q. Hussain
, F. D. Zaman
, A. H. Bokhari
, A. H. Kara^*

^*Corresponding author for this work

Department of Mathematics

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

6 Scopus citations

Abstract

We investigate the vector fields that arise from one-parameter Lie groups of transformations that leave invariant some classes of fractional nonlinear Schrödinger equation with nonlocal nonlinearity. Furthermore, the associated conserved flows are constructed. To this end, the models adopt the Riemann-Liouville fractional form on the time derivative. Surprisingly, energy conservation is not obtained but charge and momentum are.

Original language	English
Article number	165619
Journal	Optik
Volume	224
DOIs	https://doi.org/10.1016/j.ijleo.2020.165619
State	Published - Dec 2020

Bibliographical note

Publisher Copyright:
© 2020

Keywords

Fractional equations
Nonlinear
Nonlocal
Schrödinger

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Electrical and Electronic Engineering

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10.1016/j.ijleo.2020.165619

Cite this

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title = "On a study of symmetries and conservation laws of a class of time fractional Schr{\"o}dinger equations with nonlocal nonlinearities",

abstract = "We investigate the vector fields that arise from one-parameter Lie groups of transformations that leave invariant some classes of fractional nonlinear Schr{\"o}dinger equation with nonlocal nonlinearity. Furthermore, the associated conserved flows are constructed. To this end, the models adopt the Riemann-Liouville fractional form on the time derivative. Surprisingly, energy conservation is not obtained but charge and momentum are.",

keywords = "Fractional equations, Nonlinear, Nonlocal, Schr{\"o}dinger",

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doi = "10.1016/j.ijleo.2020.165619",

language = "English",

volume = "224",

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AU - Hussain, Q.

AU - Zaman, F. D.

AU - Bokhari, A. H.

AU - Kara, A. H.

PY - 2020/12

Y1 - 2020/12

N2 - We investigate the vector fields that arise from one-parameter Lie groups of transformations that leave invariant some classes of fractional nonlinear Schrödinger equation with nonlocal nonlinearity. Furthermore, the associated conserved flows are constructed. To this end, the models adopt the Riemann-Liouville fractional form on the time derivative. Surprisingly, energy conservation is not obtained but charge and momentum are.

AB - We investigate the vector fields that arise from one-parameter Lie groups of transformations that leave invariant some classes of fractional nonlinear Schrödinger equation with nonlocal nonlinearity. Furthermore, the associated conserved flows are constructed. To this end, the models adopt the Riemann-Liouville fractional form on the time derivative. Surprisingly, energy conservation is not obtained but charge and momentum are.

KW - Fractional equations

KW - Nonlinear

KW - Nonlocal

KW - Schrödinger

UR - https://www.scopus.com/pages/publications/85092091169

U2 - 10.1016/j.ijleo.2020.165619

DO - 10.1016/j.ijleo.2020.165619

M3 - Article

AN - SCOPUS:85092091169

SN - 0030-4026

VL - 224

JO - Optik

JF - Optik

M1 - 165619

ER -

On a study of symmetries and conservation laws of a class of time fractional Schrödinger equations with nonlocal nonlinearities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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