133 citations · 134 across the 3 of their papers we have counts for
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Slow motion for gradient systems with equal depth multiple-well potentials
Fabrice Bethuel, Didier Smets, Giandomenico Orlandi
For scalar reaction-diffusion in one space dimension, it is known for a long time that fronts move with an exponentially small speed for potentials with several distinct mini- mize…
On the linear wave regime of the Gross-Pitaevskii equation
Fabrice Bethuel, Raphael Danchin, Didier Smets
We study a long wave-length asymptotics for the Gross-Pitaevskii equation corresponding to perturbation of a constant state of modulus one. We exhibit lower bounds on the first occ…
Travelling waves for the Gross-Pitaevskii equation II
Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut
The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Ou…