8 citations · 10 across the 4 of their papers we have counts for
4 papers
Long-Timescale Soliton Dynamics in the Korteweg-de Vries Equation with Multiplicative Translation-Invariant Noise
Rik W. S. Westdorp, Hermen Jan Hupkes
This paper studies the behavior of solitons in the Korteweg-de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitud…
Travelling Corners for Spatially Discrete Reaction-Diffusion System
Hermen Jan Hupkes, Leonardo Morelli
We consider reaction-diffusion equations on the planar square lattice that admit spectrally stable planar travelling wave solutions. We show that these solutions can be continued i…
Entire Solutions for Bistable Lattice Differential Equations with Obstacles
A. Hoffman, H. J. Hupkes, E. Van Vleck
We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obs…
Multidimensional Stability of Waves Travelling Through Rectangular Lattices in Rational Directions
A. Hoffman, H. J. Hupkes, E. Van Vleck
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagat…