| Name | simple-idealized-1d-nlse JSON |
| Version |
0.0.4
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| download |
| home_page | None |
| Summary | A flexible and efficient solver for the 1D Nonlinear Schrödinger Equation |
| upload_time | 2025-09-07 05:39:38 |
| maintainer | None |
| docs_url | None |
| author | Sandy H. S. Herho |
| requires_python | <4.0,>=3.8 |
| license | WTFPL |
| keywords |
|
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# Simple Idealized 1D NLSE Solver
[](https://doi.org/10.5281/zenodo.16895284)
[](https://www.python.org/downloads/)
[](http://www.wtfpl.net/about/)
[](https://github.com/psf/black)
[](https://pypi.org/project/simple-idealized-1d-nlse/)
A flexible and efficient solver for the 1D Nonlinear Schrödinger Equation (NLSE) using pseudo-spectral methods
## Overview
This package provides a high-accuracy numerical framework for solving the 1D focusing NLSE:
$$i \frac{\partial \psi}{\partial t} + \frac{1}{2} \frac{\partial^2 \psi}{\partial x^2 } + |\psi|^2 \psi = 0,$$
where $\psi(x,t)$ is the complex wave function. This equation models various physical phenomena including Bose-Einstein condensates, nonlinear optics, and water waves.
### Numerical Method
The solver employs a **Fourier pseudo-spectral method** combined with high-order time integration:
#### Spatial Discretization
Using the Fourier transform $\hat{\psi}(k,t) = \mathcal{F}[\psi(x,t)]$, the NLSE becomes:
$$\frac{\partial \hat{\psi}}{\partial t} = -\frac{i}{2}k^2\hat{\psi} + i\mathcal{F}[|\psi|^2\psi],$$
where spatial derivatives are computed spectrally:
- $\mathcal{F}[\partial^2_x \psi] = -k^2 \hat{\psi}$
- Wavenumbers: $k_j = 2\pi j/L$ for $j \in [-N/2, N/2)$
#### Anti-Aliasing Filter
To prevent aliasing from the nonlinear term, we apply an exponential filter (2/3 rule):
$$\sigma(k) = \exp\left[-36\left(\frac{|k|}{k_{max}}\right)^{36}\right], \quad k_{max} = \frac{2\pi N}{3L}$$
#### Time Integration
The filtered equation in Fourier space:
$$\frac{d\hat{\psi}_f}{dt} = -\frac{i}{2}k^2\hat{\psi}_f + i\sigma(k)\mathcal{F}[|\mathcal{F}^{-1}[\hat{\psi}_f]|^2 \mathcal{F}^{-1}[\hat{\psi}_f]]$$
is solved using the **8th-order Dormand-Prince method (DOP853)** with adaptive time-stepping, achieving relative tolerances down to $10^{-9}$.
### Conservation Laws
The solver monitors three conserved quantities to ensure numerical stability:
- **Mass (L² norm)**: $M = \int_{-\infty}^{\infty} |\psi|^2 dx$
- **Momentum**: $P = \int_{-\infty}^{\infty} \text{Im}(\psi^* \partial_x \psi) dx$
- **Energy (Hamiltonian)**: $E = \int_{-\infty}^{\infty} \left[\frac{1}{2}|\partial_x \psi|^2 - \frac{1}{2}|\psi|^4\right] dx$
### Key Features
- **Spectral accuracy**: Exponential convergence for smooth solutions
- **Adaptive time-stepping**: Automatic step size control based on error estimates
- **JIT compilation**: Optional Numba acceleration for performance-critical sections
- **Stability monitoring**: Real-time tracking of conservation laws
- **Multiple initial conditions**: Solitons, breathers, and modulation instability scenarios
## Installation
### From PyPI
```bash
pip install simple-idealized-1d-nlse
```
### From source
```bash
git clone https://github.com/samuderasains/simple-idealized-1d-nlse.git
cd simple-idealized-1d-nlse
pip install -e .
```
## Quick Start
```bash
# Run single scenario with YAML config
nlse-simulate single_soliton
# Run with TXT configuration file
nlse-simulate --config configs/txt/single_soliton.txt
# Run all predefined scenarios
nlse-simulate --all
# Run with verbose output
nlse-simulate single_soliton --verbose
```
## Project Structure
```
simple_idealized_1d_nlse/
├── src/simple_idealized_1d_nlse/
│ ├── core/ # Core solver and numerical methods
│ ├── utils/ # Utility functions and helpers
│ ├── visualization/ # FiveThirtyEight-style plotting
│ └── io/ # Input/output handlers (YAML/TXT)
├── configs/
│ ├── yaml/ # YAML configuration files
│ └── txt/ # TXT configuration files
../outputs/ # Simulation results (outside package)
../logs/ # Simulation logs (outside package)
```
## Authors
- **Sandy H. S. Herho** - sandy.herho@email.ucr.edu
- **Iwan P. Anwar**
- **Faruq Khadami**
- **Rusmawan Suwarman**
- **Dasapta E. Irawan**
## License
This project is licensed under the WTFPL License - see the [LICENSE](LICENSE) file for details.
## Citation
If you use this software in your research, please cite:
```bibtex
@software{nlse_solver_2025,
title = {Simple Idealized 1D NLSE Solver},
author = {Herho, Sandy H. S. and Anwar, Iwan P. and Khadami, Faruq and
Suwarman, Rusmawan and Irawan, Dasapta E.},
year = {2025},
version = {0.0.4},
url = {https://github.com/sandyherho/simple_idealized_1d_nlse}
}
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"description": "# Simple Idealized 1D NLSE Solver\n\n[](https://doi.org/10.5281/zenodo.16895284)\n[](https://www.python.org/downloads/)\n[](http://www.wtfpl.net/about/)\n[](https://github.com/psf/black)\n[](https://pypi.org/project/simple-idealized-1d-nlse/)\n\nA flexible and efficient solver for the 1D Nonlinear Schr\u00f6dinger Equation (NLSE) using pseudo-spectral methods\n\n## Overview\n\nThis package provides a high-accuracy numerical framework for solving the 1D focusing NLSE:\n\n$$i \\frac{\\partial \\psi}{\\partial t} + \\frac{1}{2} \\frac{\\partial^2 \\psi}{\\partial x^2 } + |\\psi|^2 \\psi = 0,$$\n\nwhere $\\psi(x,t)$ is the complex wave function. This equation models various physical phenomena including Bose-Einstein condensates, nonlinear optics, and water waves.\n\n### Numerical Method\n\nThe solver employs a **Fourier pseudo-spectral method** combined with high-order time integration:\n\n#### Spatial Discretization\nUsing the Fourier transform $\\hat{\\psi}(k,t) = \\mathcal{F}[\\psi(x,t)]$, the NLSE becomes:\n\n$$\\frac{\\partial \\hat{\\psi}}{\\partial t} = -\\frac{i}{2}k^2\\hat{\\psi} + i\\mathcal{F}[|\\psi|^2\\psi],$$\n\nwhere spatial derivatives are computed spectrally:\n- $\\mathcal{F}[\\partial^2_x \\psi] = -k^2 \\hat{\\psi}$\n- Wavenumbers: $k_j = 2\\pi j/L$ for $j \\in [-N/2, N/2)$\n\n#### Anti-Aliasing Filter\nTo prevent aliasing from the nonlinear term, we apply an exponential filter (2/3 rule):\n\n$$\\sigma(k) = \\exp\\left[-36\\left(\\frac{|k|}{k_{max}}\\right)^{36}\\right], \\quad k_{max} = \\frac{2\\pi N}{3L}$$\n\n#### Time Integration\nThe filtered equation in Fourier space:\n\n$$\\frac{d\\hat{\\psi}_f}{dt} = -\\frac{i}{2}k^2\\hat{\\psi}_f + i\\sigma(k)\\mathcal{F}[|\\mathcal{F}^{-1}[\\hat{\\psi}_f]|^2 \\mathcal{F}^{-1}[\\hat{\\psi}_f]]$$\n\nis solved using the **8th-order Dormand-Prince method (DOP853)** with adaptive time-stepping, achieving relative tolerances down to $10^{-9}$.\n\n### Conservation Laws\n\nThe solver monitors three conserved quantities to ensure numerical stability:\n\n- **Mass (L\u00b2 norm)**: $M = \\int_{-\\infty}^{\\infty} |\\psi|^2 dx$\n\n- **Momentum**: $P = \\int_{-\\infty}^{\\infty} \\text{Im}(\\psi^* \\partial_x \\psi) dx$\n\n- **Energy (Hamiltonian)**: $E = \\int_{-\\infty}^{\\infty} \\left[\\frac{1}{2}|\\partial_x \\psi|^2 - \\frac{1}{2}|\\psi|^4\\right] dx$\n\n### Key Features\n\n- **Spectral accuracy**: Exponential convergence for smooth solutions\n- **Adaptive time-stepping**: Automatic step size control based on error estimates\n- **JIT compilation**: Optional Numba acceleration for performance-critical sections\n- **Stability monitoring**: Real-time tracking of conservation laws\n- **Multiple initial conditions**: Solitons, breathers, and modulation instability scenarios\n\n## Installation\n\n### From PyPI\n\n```bash\npip install simple-idealized-1d-nlse\n```\n\n\n### From source\n\n```bash\ngit clone https://github.com/samuderasains/simple-idealized-1d-nlse.git\ncd simple-idealized-1d-nlse\npip install -e .\n```\n\n## Quick Start\n\n```bash\n# Run single scenario with YAML config\nnlse-simulate single_soliton\n\n# Run with TXT configuration file\nnlse-simulate --config configs/txt/single_soliton.txt\n\n# Run all predefined scenarios\nnlse-simulate --all\n\n# Run with verbose output\nnlse-simulate single_soliton --verbose\n```\n\n## Project Structure\n\n```\nsimple_idealized_1d_nlse/\n\u251c\u2500\u2500 src/simple_idealized_1d_nlse/\n\u2502 \u251c\u2500\u2500 core/ # Core solver and numerical methods\n\u2502 \u251c\u2500\u2500 utils/ # Utility functions and helpers\n\u2502 \u251c\u2500\u2500 visualization/ # FiveThirtyEight-style plotting\n\u2502 \u2514\u2500\u2500 io/ # Input/output handlers (YAML/TXT)\n\u251c\u2500\u2500 configs/ \n\u2502 \u251c\u2500\u2500 yaml/ # YAML configuration files\n\u2502 \u2514\u2500\u2500 txt/ # TXT configuration files\n\n../outputs/ # Simulation results (outside package)\n../logs/ # Simulation logs (outside package)\n```\n\n\n## Authors\n\n- **Sandy H. S. Herho** - sandy.herho@email.ucr.edu\n- **Iwan P. Anwar** \n- **Faruq Khadami** \n- **Rusmawan Suwarman** \n- **Dasapta E. Irawan** \n\n## License\n\nThis project is licensed under the WTFPL License - see the [LICENSE](LICENSE) file for details.\n\n## Citation\n\nIf you use this software in your research, please cite:\n\n```bibtex\n@software{nlse_solver_2025,\n title = {Simple Idealized 1D NLSE Solver},\n author = {Herho, Sandy H. S. and Anwar, Iwan P. and Khadami, Faruq and \n Suwarman, Rusmawan and Irawan, Dasapta E.},\n year = {2025},\n version = {0.0.4},\n url = {https://github.com/sandyherho/simple_idealized_1d_nlse}\n}\n",
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