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https://github.com/omelchert/pyGLLE

Python package for temporal evolution of initial conditions under the generalized Lugiato-Lefever equation
https://github.com/omelchert/pyGLLE

computational-physics lugiato-lefever-equation partial-differential-equations pseudospectral-methods python scientific-software

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Python package for temporal evolution of initial conditions under the generalized Lugiato-Lefever equation

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README 

        
# pyGLLE



[![License: MIT](https://img.shields.io/badge/License-MIT-green.svg)](https://opensource.org/licenses/MIT)



pyGLLE is a Python toolkit for simulating the propagation dynamics of

dissipative solitons in a variant of the 

[Lugiato-Lefever equation](https://en.wikipedia.org/wiki/Lugiato–Lefever_equation) (LLE).

Including dispersion terms of third and fourth order, this variant is here

referred to as the generalised LLE (GLLE).



The provided software implements a solver for a variant of the LLE including

dispersion terms of third and fourth order. It also includes the functionality

to solve for stationary solutions of the standard LLE, containing one or

several localized dissipative structures.



### Prerequisites



The tools provided by the `pyGLLE` package require the functionality of 



* numpy (>=1.8.0rc1)

* scipy (>=0.13.0b1)



Further, the figure generation scripts included with the examples require the

funcality of



* matplotlib (>=1.2.1)



## Included materials



The repository follows a modular structure:



```

pyGLLE/

├── LICENSE.md

├── README.md

├── numExp01_stationarySolution

│   ├── data_stationary_solution

│   ├── main_findStationarySolution.py

│   ├── pp_figure

│   │   ├── FIGS

│   │   ├── generateFigure.sh

│   │   └── main_figure_stationarySolution.py

│   └── run.sh

├── numExp02_propagationScenarios

│   ├── data

│   ├── data_stationary_solution

│   ├── main_findStationarySolution.py

│   ├── main_propagateInitialCondition.py

│   ├── pp_figure_propagationScenarios

│   │   ├── FIGS

│   │   ├── figure_base_propagationDynamics.py

│   │   ├── generateFigures.sh

│   │   └── main_figure_propagationDynamics_stationarySolution.py

│   └── run.sh

├── scripts

│   └── pyGLLE.py

└── src

    ├── data_handler.py

    ├── solver.py

    └── stationary_solution.py

```



Subfolder `/src` contains Python modules implementing the basic functionality of the software:

* `data_handler.py`: provides a class, handling data accumulation and data

* ouput. Output data is stored using the numpy native npz-format.

* `stationary_solution.py`:

    provides functions allowing to obtain stationary localized solution of the standard LLE.

* `solver.py`: implements a solver for the numerical integration of the generalized LLE using a Runge-Kutta method.



The folder `/scripts` contains the main Python module implementing the

interface between the user supplied code and the algorithms and data structures

contained in the modules in folder `\src`:

* `pyGLLE.py`: defines the main functions `findStationarySolution` and

    `propagateInitialCondition`.



Further, the folders `\numExp01_stationarySolution` and

`\numExp02_propagationScenarios` contain scripts that implement example

workflows ranging from the specification of a propagation scenario to the

visualization of the generated raw data.



The repository further contains

* `LICENSE`, a license file.

* `Readme.md`, this file.



For a more detailed description of functions, defined in the above modules,

their parameters and return values we refer to the example cases and

documentation provided within the code.



## Availability of the software



The pyGLLE software package is derived from our research software and is meant to work as a (system-)local software tool. There is no need to install it once you got a local [clone](https://help.github.com/en/github/creating-cloning-and-archiving-repositories/cloning-a-repository) of the repository, e.g. via



``$ git clone https://github.com/omelchert/pyGLLE``



We further prepared a [pyGLLE compute capsule](https://codeocean.com/capsule/e0ed77d4-9589-45b4-abc8-3b21f3ce92c8/) on [Code Ocean](https://codeocean.com), allowing to directly run and modify an exemplary simulation without the need to create a local copy of the repository. 



## Links



The pyGLLE software package is described in 



> O. Melchert, A. Demircan, "pyGLLE: A Python toolkit for solving the generalized Lugiato–Lefever equation," SoftwareX 15 (2021) 100741, DOI: [10.1016/j.softx.2021.100741](https://doi.org/10.1016/j.softx.2021.100741).



The presented software has been extensively used in our research work,

including the study of resonant emission of multi-frequency radiation by

oscillating dissipative solitons in the LLE including third order dispersion



> O. Melchert, A. Demircan, A. Yulin, "Multi-frequency radiation of dissipative solitons in optical fiber cavities," Scientific Reports 10 (2020) 8849, DOI: [10.1038/s41598-020-65426-x](https://doi.org/10.1038/s41598-020-65426-x).



and the dynamics of localized dissipative structures in the generalized LLE with negative quartic group-velocity dispersion 



> O. Melchert, A. Yulin, A. Demircan, "Dynamics of localized dissipative structures in a generalized Lugiato-Lefever model with negative quartic group-velocity dispersion," Optics Letters 45 (2020) 2764, DOI: [10.1364/OL.392180](https://www.doi.org/10.1364/OL.392180).



## License



This project is licensed under the MIT License - see the [LICENSE.md](LICENSE.md) file for details.



## Acknowledgments



This work received funding from the Deutsche Forschungsgemeinschaft  (DFG) under

Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD

(Photonics, Optics, and Engineering – Innovation Across Disciplines) (EXC 2122,

projectID 390833453).