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math.AP2008
Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation
Patrick Gerard, Zhifei Zhang
In this paper, we prove the nonlinear orbital stability of the stationary traveling wave of the one-dimensional Gross-Pitaevskii equation by using Zakharov-Shabat's inverse scatter…
math.AP2003★ 5 cited
Multilinear eigenfunction estimates for the Laplace spectral projectors on compact manifolds
N. Burq, P. Gerard, N. Tzvetkov
The purpose of this note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained in a…