SpectraVVave: Compute traveling waves

Getting started

Here is a simple example to get started with SpectraVVave:

We first import the relevant bits in SpectraVVave:

from travwave.diagram import BifurcationDiagram
import travwave.equations as teq
import travwave.boundary as tbc

Define the half length of the travelling wave:

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.

boundary_cond = tbc.Minimum()

Setup the diagram object, initialize and run it:

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:

bd.plot_solution(bd.navigation[-1]['solution'])

We refine to get a higher resolution travelling wave:

new_size = 500
refined, v, parameter = bd.navigation.refine_at(new_size)

and we plot that refined solution:

bd.plot_solution(refined)

We plot the bifurcation diagram, as well as the last refined parameter:

bd.nplot_diagram()
plt.plot(parameter[0], parameter[1], 'or')