Preprint of the project:
08-010 Gabriel J. Lord, Vera Thümmler.
Freezing stochastic travelling waves
We consider in this paper a new method for computing stochastic travelling waves that freezes
the wave in the computational domain so it does not move. We obtain a stochastic partial differential algebraic
equation that we then discretize and solve. We compare this to a standard approach of simply solving a stochastic
partial differential equation directly and examine wave profiles and wave speeds for the Nagumo equation. We
examine the effect of multiplicative and additive noise on the speed of propagation with the noise intensity. For
multiplicative Itô noise the wave speed is not always strictly increasing with noise intensity. We illustrate that the
method can be applied when nucleation of new stochastic travelling waves occurs with additive noise. Finally we
compute using a weaker notion of wave speed to freeze the travelling wave.
