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math.DS2025
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…
math.DS2017★ 1 cited
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…