133 citations · 184 across the 9 of their papers we have counts for
8 papers · 1 filter
Asymptotics for two-dimensional vectorial Allen-Cahn systems
Fabrice Bethuel
The formation of codimension-one interfaces for multi-well gradient-driven problems is well-known and established in the scalar case, where the equation is often referred to as the…
Concentration sets for multiple equal-depth wells potentials in the 2D elliptic case
Fabrice Bethuel
The formation of codimension-one interfaces for multiwell gradient-driven problems is well-known and established in the scalar case, where the equation is often referred to as the…
The motion law of fronts for scalar reaction-diffusion equations with multiple wells : the degenerate case,
Fabrice Bethuel, Didier Smets
We derive a precise motion law for fronts of solutions to scalar one-dimensional reaction-diffusion equations with equal depth multiple-wells, in the case the second derivative of…
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 Korteweg-de Vries long-wave approximation of the Gross-Pitaevskii equation II
Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut +1
In this paper, we proceed along our analysis of the Korteweg-de Vries approximation of the Gross-Pitaevskii equation initiated in a previous paper. At the long-wave limit, we estab…
On the Korteweg-de Vries long-wave approximation of the Gross-Pitaevskii equation I
Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut +1
The fact that the Korteweg-de-Vries equation offers a good approximation of long-wave solutions of small amplitude to the one-dimensional Gross-Pitaevskii equation was derived seve…