pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation

Oliver Melchert; Ayhan Demircan

doi:10.1016/j.softx.2021.100741

pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation

Oliver Melchert^*
, Ayhan Demircan

^*Corresponding author for this work

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

Abstract

We present a Python toolkit for simulating the propagation dynamics of dissipative solitons in a variant of the Lugiato–Lefever equation (LLE) including dispersion terms of third and fourth order. In addition, the provided software allows to prepare initial conditions given by stationary localized solutions of the standard LLE in the anomalous group-velocity dispersion regime. Propagation scenarios for custom control parameters and initial conditions can be specified by the user via a simple class data structure. We demonstrate the implemented functionality by showing how to obtain stationary solutions of the standard LLE containing a dissipative soliton, and, demonstrating different characteristic propagation scenarios. The pyGLLE software package is open-source and released under the X11 License in a publicly available software repository.

Original language	English
Article number	100741
Journal	SoftwareX
Volume	15
E-pub ahead of print	5 Jul 2021
DOIs	https://doi.org/10.1016/j.softx.2021.100741
Publication status	Published - Jul 2021

Keywords

Dissipative solitons
Lugiato–Lefever equation
Nonlinear partial differential equations
Python

ASJC Scopus subject areas

Software
Computer Science Applications

Access to Document

10.1016/j.softx.2021.100741Licence: CC BY 4.0

Cite this

@article{1817223e18784be9969c0b888f18e4a6,

title = "pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation",

abstract = "We present a Python toolkit for simulating the propagation dynamics of dissipative solitons in a variant of the Lugiato–Lefever equation (LLE) including dispersion terms of third and fourth order. In addition, the provided software allows to prepare initial conditions given by stationary localized solutions of the standard LLE in the anomalous group-velocity dispersion regime. Propagation scenarios for custom control parameters and initial conditions can be specified by the user via a simple class data structure. We demonstrate the implemented functionality by showing how to obtain stationary solutions of the standard LLE containing a dissipative soliton, and, demonstrating different characteristic propagation scenarios. The pyGLLE software package is open-source and released under the X11 License in a publicly available software repository.",

keywords = "Dissipative solitons, Lugiato–Lefever equation, Nonlinear partial differential equations, Python",

author = "Oliver Melchert and Ayhan Demircan",

note = "Funding Information: We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG), Germany under Germany{\textquoteright}s Excellence Strategy within the Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines) (EXC 2122, projectID 390833453 ). The publication of this article was funded by the Open Access Fund of the Leibniz Universit{\"a}t Hannover . ",

year = "2021",

month = jul,

doi = "10.1016/j.softx.2021.100741",

language = "English",

volume = "15",

journal = "SoftwareX",

issn = "2352-7110",

publisher = "Elsevier BV",

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T1 - pyGLLE

T2 - A Python toolkit for solving the generalized Lugiato–Lefever equation

AU - Melchert, Oliver

AU - Demircan, Ayhan

N1 - Funding Information: We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG), Germany under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines) (EXC 2122, projectID 390833453 ). The publication of this article was funded by the Open Access Fund of the Leibniz Universität Hannover .

PY - 2021/7

Y1 - 2021/7

N2 - We present a Python toolkit for simulating the propagation dynamics of dissipative solitons in a variant of the Lugiato–Lefever equation (LLE) including dispersion terms of third and fourth order. In addition, the provided software allows to prepare initial conditions given by stationary localized solutions of the standard LLE in the anomalous group-velocity dispersion regime. Propagation scenarios for custom control parameters and initial conditions can be specified by the user via a simple class data structure. We demonstrate the implemented functionality by showing how to obtain stationary solutions of the standard LLE containing a dissipative soliton, and, demonstrating different characteristic propagation scenarios. The pyGLLE software package is open-source and released under the X11 License in a publicly available software repository.

AB - We present a Python toolkit for simulating the propagation dynamics of dissipative solitons in a variant of the Lugiato–Lefever equation (LLE) including dispersion terms of third and fourth order. In addition, the provided software allows to prepare initial conditions given by stationary localized solutions of the standard LLE in the anomalous group-velocity dispersion regime. Propagation scenarios for custom control parameters and initial conditions can be specified by the user via a simple class data structure. We demonstrate the implemented functionality by showing how to obtain stationary solutions of the standard LLE containing a dissipative soliton, and, demonstrating different characteristic propagation scenarios. The pyGLLE software package is open-source and released under the X11 License in a publicly available software repository.

KW - Dissipative solitons

KW - Lugiato–Lefever equation

KW - Nonlinear partial differential equations

KW - Python

UR - https://www.scopus.com/pages/publications/85109070151

U2 - 10.1016/j.softx.2021.100741

DO - 10.1016/j.softx.2021.100741

M3 - Article

AN - SCOPUS:85109070151

SN - 2352-7110

VL - 15

JO - SoftwareX

JF - SoftwareX

M1 - 100741

ER -

pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

PhoenixD: Cluster of Excellence 2122/1: Photonics, Optics, and Engineering – Innovation Across Disciplines

Cite this

pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Projects

PhoenixD: Cluster of Excellence 2122/1: Photonics, Optics, and Engineering – Innovation Across Disciplines

Cite this