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https://github.com/olivierverdier/spectravvave
Python project to compute bifurcation diagrams of travelling waves
https://github.com/olivierverdier/spectravvave
Last synced: about 5 hours ago
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Python project to compute bifurcation diagrams of travelling waves
- Host: GitHub
- URL: https://github.com/olivierverdier/spectravvave
- Owner: olivierverdier
- License: bsd-3-clause
- Created: 2014-10-24T09:18:58.000Z (about 10 years ago)
- Default Branch: main
- Last Pushed: 2024-09-11T09:30:41.000Z (2 months ago)
- Last Synced: 2024-09-11T13:03:32.842Z (2 months ago)
- Language: Python
- Size: 879 KB
- Stars: 4
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
Awesome Lists containing this project
README
# SpectraVVave: Compute traveling waves
[](https://github.com/olivierverdier/SpecTraVVave/actions/workflows/python_package.yml?query=branch%3Amain)
[](https://codecov.io/github/olivierverdier/SpecTraVVave)
[](https://arxiv.org/abs/1606.01465)
## Getting started
Here is a simple example to get started with SpectraVVave:
We first import the relevant bits in SpectraVVave:
```python
from travwave.diagram import BifurcationDiagram
import travwave.equations as teq
import travwave.boundary as tbc
```
Define the half length of the travelling wave:
```python
length = 30
```
Which equation are we solving. Look in the `travwave/equations` folder, or implement your own equation. Here we choose the KDV equation.
```
equation = teq.kdv.KDV(length)
```
Which boundary condition are we using? You will find some possible boundary conditions in `travwave/bounday`, or you can implement your own. Here we use the `Minimum` boundary condition, which enforces the minimum to be at zero.
```python
boundary_cond = tbc.Minimum()
```
Setup the diagram object, initialize and run it:
```python
bd = BifurcationDiagram(equation, boundary_cond)
# initialize it with default parameters
bd.initialize()
# run for fifty steps
bd.navigation.run(50)
```
Let us see what the amplitude reached is:
```
print('Amplitude = ', bd.navigation[-1]['parameter'][bd.navigation.amplitude_])
```
We plot the current computed solution, at coarse resolution:
```python
bd.plot_solution(bd.navigation[-1]['solution'])
```
We refine to get a higher resolution travelling wave:
```python
new_size = 500
refined, v, parameter = bd.navigation.refine_at(new_size)
```
and we plot that refined solution:
```python
bd.plot_solution(refined)
```
We plot the bifurcation diagram, as well as the last refined parameter:
```python
bd.nplot_diagram()
plt.plot(parameter[0], parameter[1], 'or')
```
