13 papers · 1 filter
Stability of Stochastically Forced Solitons in the Korteweg-de Vries Equation
Rik W. S. Westdorp, Hermen Jan Hupkes
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statist…
Local Phase Tracking and Metastability of Planar Waves in Stochastic Reaction-Diffusion Systems
Mark van den Bosch, Hermen Jan Hupkes
Planar travelling waves on with are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescale…
Conditional Speed and Shape Corrections for Travelling Wave Solutions to Stochastically Perturbed Reaction-Diffusion Systems
Mark van den Bosch, Christian H. S. Hamster, Hermen Jan Hupkes
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equatio…
Multidimensional Stability of Planar Travelling Waves for Stochastically Perturbed Reaction-Diffusion Systems
Mark van den Bosch, Hermen Jan Hupkes
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invarian…
Soliton Amplification in the Korteweg-de Vries Equation by Multiplicative Forcing
Rik W. S. Westdorp, Hermen Jan Hupkes
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation with small multiplicative forcing. Forcing breaks the conservative structure of the KdV equa…
Propagation reversal on trees in the large diffusion regime
Hermen Jan Hupkes, Mia Jukic
In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite -ary trees in the continuum regime where the diffusion parameter is large…