nextuppreviouscontents
Next:Thrid bifurcationUp:Bifurcation of KSEPrevious:Unlinear stabilityContents

Second bifurcation

Before presenting this new bifurcation, I would like explain the way I have realised the simulation. If I had start all the simulation with a small perturbation, the time of calculation would have been too long. That's why I use for the initialisation of the simulation for $ \nu+\Delta \nu$ the solution converged for $ \nu $.

With this strategy, it's easier to obtain the new convergence.

When the parameter $ \nu $ rich the value $ 130$, the simulation converged toward a solution which looks like those of the first bifurcation, but the difference is that this solution is travelling on the domain. The speed of the solution is constant and increase with $ \nu $. The animation below show the travilling wave for $ \nu = 140$.
 

The graph of norm versus time is on the figure 3.3.

\includegraphics [scale=0.8]{norm140.eps}
Figure 3.3: Norm versus time for $ \nu = 140$
We can remark that the norm is not a constant. It's due to a numerical problem, but it is not important to understand the phenomenon. Moreover it allows us to calculate the speed of the wave. In fact the periodicity of the norm is directly link to the speed of wave.


nextuppreviouscontents
Next:Thrid bifurcationUp:Bifurcation of KSEPrevious:Unlinear stabilityContents
Julien Delbove

2000-11-23