1 citations · 2 across the 3 of their papers we have counts for
3 papers
From heteroclinic loops to homoclinic snaking in reversible systems: rigorous forcing through computer-assisted proofs
Jan Bouwe van den Berg, Gabriel William Duchesne, Jean-Philippe Lessard
Homoclinic snaking is a widespread phenomenon observed in many pattern-forming systems. Demonstrating its occurrence in non-perturbative regimes has proven difficult, although a fo…
Periodic localized traveling waves in the two-dimensional suspension bridge equation
Lindsey van der Aalst, Jan Bouwe van den Berg, Jean-Philippe Lessard
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional ca…
A Floer homology approach to travelling waves in reaction-diffusion equations on cylinders
Bente Bakker, Jan Bouwe van den Berg, Rob Vandervorst
We develop a new homological invariant for the dynamics of the bounded solutions to the travelling wave PDE \[ \left\{ \begin{array}{l l} \partial_t^2 u - c \partial_t u + Δu + f(x…