Gross???Pitaevskii dynamics of Bose???Einstein condensates and superfluid turbulence, Fluid Dynamics Research, vol.33, issue.5-6, pp.5-6, 2003. ,
DOI : 10.1016/j.fluiddyn.2003.09.001
Topological methods for the Ginzburg-Landau equations, Journal de Math??matiques Pures et Appliqu??es, vol.77, issue.1, p.149, 1998. ,
DOI : 10.1016/S0021-7824(98)80064-0
Stability of the soliton-like ???bubbles???, Physica D: Nonlinear Phenomena, vol.34, issue.1-2, pp.240-254, 1989. ,
DOI : 10.1016/0167-2789(89)90237-6
Soliton-like ???bubbles??? in a system of interacting bosons, Physics Letters A, vol.128, issue.1-2, pp.52-56, 1988. ,
DOI : 10.1016/0375-9601(88)91042-0
Quantised vortices, travelling coherent structures and superfluid turbulence, in Stationary and time dependent Gross-Pitaevskii equations, Contemp. Math, vol.473, pp.26-54, 2008. ,
On the KP-I transonic limit of twodimensional Gross-Pitaevskii travelling waves, Dynamics of PDE, vol.5, issue.3, pp.241-280, 2008. ,
Travelling Waves for the Gross-Pitaevskii Equation II, Communications in Mathematical Physics, vol.151, issue.4, pp.567-651, 2009. ,
DOI : 10.1007/s00220-008-0614-2
Vortex rings for the Gross-Pitaevskii equation, Journal of the European Mathematical Society, vol.6, pp.17-94, 2004. ,
DOI : 10.4171/JEMS/2
Travelling waves for the Gross-Pitaevskii equation I, Ann, Inst. H. Poincaré Phys. Théor, vol.70, pp.147-238, 1999. ,
Analyse fonctionnelle, 1983. ,
Lifting in Sobolev Spaces, Journal d'Analyse Mathématique, vol.80, pp.37-86, 2000. ,
Minimum action solutions of some vector field equations, Communications in Mathematical Physics, vol.22, issue.I, pp.97-113, 1984. ,
DOI : 10.1007/BF01217349
Orbital stability of standing waves for some nonlinear Schr???dinger equations, Communications in Mathematical Physics, vol.49, issue.4, pp.549-561, 1982. ,
DOI : 10.1007/BF01403504
Travelling waves for the Gross???Pitaevskii equation in dimension larger than two, Nonlinear Analysis: Theory, Methods & Applications, vol.58, issue.1-2, pp.175-204, 2004. ,
DOI : 10.1016/j.na.2003.10.028
URL : https://hal.archives-ouvertes.fr/hal-00876577
Travelling waves for the nonlinear Schr??dinger equation with general nonlinearity in dimension one, Nonlinearity, vol.25, issue.3, pp.813-850, 2012. ,
DOI : 10.1088/0951-7715/25/3/813
Rarefaction pulses for the Nonlinear Schrödinger Equation in the transonic limit, Comm. Math. Phys ,
Travelling waves for the Nonlinear Schrödinger Equation with general nonlinearity in dimension two, preprint, 2013. ,
Nonlinear Schr??dinger equation and superfluid hydrodynamics, The European Physical Journal B, vol.1, issue.2, pp.245-253, 1998. ,
DOI : 10.1007/s100510050178
Solitary waves of generalized Kadomtsev-Petviashvili equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.14, issue.2, pp.211-236, 1997. ,
DOI : 10.1016/S0294-1449(97)80145-X
Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves, SIAM Journal on Mathematical Analysis, vol.28, issue.5, pp.1064-1085, 1997. ,
DOI : 10.1137/S0036141096297662
Non-existence for travelling waves with small energy for the Gross???Pitaevskii equation in dimension, Comptes Rendus Mathematique, vol.347, issue.7-8, pp.347-375, 2009. ,
DOI : 10.1016/j.crma.2009.02.006
Measure theory and fine properties of functions, 1992. ,
The Cauchy Problem for Defocusing Nonlinear Schr??dinger Equations with Non-Vanishing Initial Data at Infinity, Communications in Partial Differential Equations, vol.1, issue.5, pp.729-771, 2008. ,
DOI : 10.1007/BF00971094
The Cauchy problem for the Gross???Pitaevskii equation, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.23, issue.5, pp.765-779, 2006. ,
DOI : 10.1016/j.anihpc.2005.09.004
The Gross-Pitaevskii equation in the energy space, Contemp. Math, vol.473, pp.129-148, 2008. ,
DOI : 10.1090/conm/473/09226
Elliptic Partial Differential Equations of Second Order, 2001. ,
Motions in a Bose condensate. III. The structure and effective masses of charged and uncharged impurities, Journal of Physics A: Mathematical, Nuclear and General, vol.7, issue.2, pp.260-279, 1974. ,
DOI : 10.1088/0305-4470/7/2/012
A Non-Existence Result for Supersonic Travelling Waves in the Gross-Pitaevskii Equation, Communications in Mathematical Physics, vol.243, issue.1, pp.93-103, 2003. ,
DOI : 10.1007/s00220-003-0961-y
Hydrodynamics of a Superfluid Condensate, Journal of Mathematical Physics, vol.4, issue.2, pp.195-207, 1963. ,
DOI : 10.1063/1.1703944
Three-dimensional solitons in He II, JETP Lett, vol.27, issue.10, pp.535-538, 1978. ,
Motions in a Bose condensate. IV. Axisymmetric solitary waves, Journal of Physics A: Mathematical and General, vol.15, issue.8, pp.2599-2619, 1982. ,
DOI : 10.1088/0305-4470/15/8/036
Motions in a Bose condensate. V. Stability of solitary wave solutions of non-linear Schrodinger equations in two and three dimensions, Journal of Physics A: Mathematical and General, vol.19, issue.15, pp.2991-3011, 1986. ,
DOI : 10.1088/0305-4470/19/15/023
IntroductionàIntroduction`Introductionà la théorie des points critiques et applications auxprobì emes elliptiques, 1993. ,
Global well-posedness of the Gross???Pitaevskii and cubic-quintic nonlinear Schr??dinger equations with non-vanishing boundary conditions, Mathematical Research Letters, vol.19, issue.5, pp.969-986, 2012. ,
DOI : 10.4310/MRL.2012.v19.n5.a1
Dark optical solitons: physics and applications, Physics Reports, vol.298, issue.2-3, pp.81-197, 1998. ,
DOI : 10.1016/S0370-1573(97)00073-2
Self-focusing of plane dark solitons in nonlinear defocusing media, Phys. Rev. E, vol.51, issue.5, pp.5016-5026, 1995. ,
On the lowest eigenvalue of the Laplacian for the intersection of two domains, Inventiones Mathematicae, vol.8, issue.3, pp.441-448, 1983. ,
DOI : 10.1007/BF01394245
The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. * *Mp denotes the Marcinkiewicz space or weak Lp space, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.1, issue.2, pp.109-145, 1984. ,
DOI : 10.1016/S0294-1449(16)30428-0
Radial Symmetry of Minimizers for Some Translation and Rotation Invariant Functionals, Journal of Differential Equations, vol.124, issue.2, pp.378-388, 1996. ,
DOI : 10.1006/jdeq.1996.0015
Nonexistence of Supersonic Traveling Waves for Nonlinear Schr??dinger Equations with Nonzero Conditions at Infinity, SIAM Journal on Mathematical Analysis, vol.40, issue.3, pp.1076-1103, 2008. ,
DOI : 10.1137/070711189
On the Symmetry of Minimizers, Archive for Rational Mechanics and Analysis, vol.18, issue.6, pp.311-330, 2009. ,
DOI : 10.1007/s00205-008-0136-2
URL : https://hal.archives-ouvertes.fr/hal-00481373
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity, Ann, Math, vol.178, issue.1, pp.107-182, 2013. ,
Nonlinear Schrödinger equation as a model of superfluid helium Quantized Vortex Dynamics and Superfluid Turbulence, Lecture Notes in Physics, vol.571, 2001. ,
Singular Integrals and Differentiability Properties of Functions, 1970. ,