J. M. Ball and V. J. Mizel, One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Rat. Mech. Anal, vol.90, issue.4, pp.325-388, 1985.

T. Bartsch, T. Weth, and M. Willem, Partial symmetry of least energy nodal solutions to some variational problems, J. Anal. Math, vol.96, pp.1-18, 2005.

H. Berestycki and P. Lions, Nonlinear scalar field equations, I. Existence of a ground state, Arch. Rat. Mech. Anal, vol.82, pp.313-345, 1983.

F. Brock, Positivity and radial symmetry of solutions to some variational problems in R N, J. Math. Anal. Appl, vol.296, pp.226-243, 2004.

Y. Chen and L. Wu, Second Order Elliptic Equations and Elliptic Systems, Translations of Mathematical Monographs, vol.174, 1998.

A. Ferrero and F. Gazzola, On subcriticality assumptions for the existence of ground states of quasilinear elliptic equations, Adv. Diff. Eq, vol.8, issue.9, pp.1081-1106, 2003.

M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, 1983.

M. Giaquinta, Introduction to the Regularity Theory for Nonlinear Elliptic Systems, 1993.

D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol.2, 1983.

O. A. Ladyzhenskaya and N. N. , Ural'tseva, Linear and quasilinear elliptic equations, 1968.

O. Lopes, Radial symmetry of minimizers for some translation and rotation invariant functionals, J. Diff. Eq, vol.124, pp.378-388, 1996.

O. Lopes, Radial and nonradial minimizers for some radially symmetric functionals, Eletr. J. Diff. Eq, issue.3, pp.1-14, 1996.

O. Lopes and M. Mari?, Symmetry of minimizers for some nonlocal variational problems, J. Functional Analysis, vol.254, issue.2, pp.535-592, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00481419

J. Malý and W. P. Ziemer, Fine Regularity of Solutions of Elliptic Partial Differential Equations, Mathematical Surveys and Monographs, 1997.

F. Pacella and T. Weth, Symmetry of solutions to semilinear elliptic equations via Morse index, Proc. AMS, vol.135, issue.6, pp.1753-1762, 2007.

P. Pucci, J. Serrin, and H. Zou, A strong maximum principle and a compact support principle for singular elliptic inequalities, J. Math. Pures Appl, vol.78, pp.769-789, 1999.

D. Smets and M. Willem, Partial symmetry and asymptotic behavior for some elliptic variational problems, Calc. Var, vol.18, pp.57-75, 2003.

E. H. Spanier, Algebraic Topology, 1966.

H. Berestycki and P. Lions, Nonlinear scalar field equations, I. Existence of a ground state, Arch. Rational Mech. Anal, vol.82, pp.313-345, 1983.

H. Berestycki, T. Gallouët, and O. Kavian, Equations de champs scalaires euclidens non linéaires dans le plan, C.R. Acad. Sc. Paris Série I -Math, vol.297, pp.307-310, 1983.

H. Brézis and E. H. Lieb, Minimum Action Solutions of Some Vector Field Equations, Comm. Math. Phys, vol.96, pp.97-113, 1984.

J. Byeon and Z. Wang, Symmetry breaking of extremal functions for the CaffarelliKohn-Nirenberg inequalities, Comm. Contemp. Math, vol.4, pp.457-465, 2002.

F. Brock, Positivity and radial symmetry of solutions to some variational problems in R N, J. Math. Anal. Appl, vol.296, pp.226-243, 2004.

J. E. Brothers and W. P. Ziemer, Minimal rearrangements of Sobolev functions, J. reine angew. Math, vol.384, pp.153-179, 1988.

J. Busca and B. Sirakov, Symmetry results for semilinear elliptic systems in the whole space, J. Diff. Eq, vol.163, issue.1, pp.41-56, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00004758

L. Damascelli, F. Pacella, and M. Ramaswamy, Symmetry of ground states of p-Laplace equations via the moving plane method, Arch. Rational Mech. Anal, vol.148, pp.291-308, 1999.

A. Ferrero and F. Gazzola, On subcriticality assumptions for the existence of ground states of quasilinear elliptic equations, Adv. Diff. Eq, vol.8, issue.9, pp.1081-1106, 2003.

M. Flucher and S. Müller, Radial symmetry and decay rate of variational ground states in the zero mass case, SIAM. J. Math. Anal, vol.29, issue.3, pp.712-719, 1998.

B. Gidas, W. N. Ni, and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in R n, Adv. Math. Supp. Stud, vol.7, pp.369-403, 1981.

P. L. Lions, The concentration-compactness principle in the Calculus of Variations, The locally compact case, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.2, pp.223-283, 1984.

O. Lopes, Radial symmetry of minimizers for some translation and rotation invariant functionals, J. Diff. Eq, vol.124, pp.378-388, 1996.

O. Lopes and M. Montenegro, Symmetry of mountain pass solutions for some vector field equations, J. Dyn. Diff. Eq, vol.18, issue.4, pp.991-999, 2006.

M. Mari?, On the symmetry of minimizers, Arch. Rational Mech. Anal

J. Serrin and H. Zou, Symmetry of ground states of quasilinear elliptic equations, Arch. Rational Mech. Anal, vol.148, pp.265-290, 1999.

J. Albert, J. L. Bona, and M. Restrepo, Solitary wave solutions of the Benjamin equation, SIAM J. Appl. Math, vol.59, issue.6, pp.2139-2161, 1999.

J. Albert, J. L. Bona, and J. Saut, Model equations for waves in stratified fluids, Proc. Roy. Soc. London A, vol.453, pp.1233-1260, 1997.

J. Angulo and F. Montenegro, Existence and evennes of solitary wave-solutions for an equation of short and long dispersive waves, Nonlinearity, vol.13, issue.5, pp.1595-1611, 2000.

A. De-bouard, Stability and instability of some nonlinear dispersive solitary waves in higher dimensions, Proc. Royal Society of Edinburgh, vol.126, pp.89-112, 1996.

F. Brock, A general rearragement inequalityà la Hardy-Littlewood, J. Inequal. Appl, vol.5, issue.4, pp.309-320, 2000.

J. Brothers and W. Ziemer, Minimal rearrangements of Sobolev functions, J. Reine Angew. Math, vol.384, pp.153-179, 1988.

J. Busca and B. Sirakov, Symmetry results for semilinear elliptic systems in the whole space, J. Differential Equations, vol.163, issue.1, pp.41-56, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00004758

H. Cartan, Théorieélémentaire des fonctions analytiques d'une ou plusieurs variables complexes, 1961.

T. Cazenave and P. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys, vol.85, pp.549-561, 1982.

R. Cipolatti, On the existence of standing waves for a Davey-Stewartson system, Comm. Partial Differential Equations, vol.17, issue.5-6, pp.967-988, 1992.

B. Gidas, W. Ni, and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in R N, Advances in Math. Suppl. Studies, vol.7, pp.369-402, 1981.

B. Guo and W. Baoxiang, The Cauchy problem for Davey-Stewartson systems, Comm. Pure Appl. Math, vol.LII, pp.1477-1490, 1999.

L. Hörmander, Linear Partial Differential Operators, 1969.

B. Kawohl, Symmetry or not ?, Mathematical Intelligencer, vol.20, pp.16-22, 1998.

E. Lieb, Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation, Studies in Appl. Math, vol.57, issue.2, pp.93-106, 1977.

E. Lieb and M. Loss, Graduate Studies in Mathematics, vol.14, 1996.

P. Lions, The Concentration-Compactness Principle in the Calculus of Variations, Ann. Inst. H. Poincaré, Anal. Non Linéaire, vol.1, pp.223-283, 1984.

O. Lopes, Radial symmetry of minimizers for some translation and rotation invariant functionals, J. Diff. Eq, vol.124, pp.378-388, 1996.

O. Lopes, Radial and nonradial minimizers for some radially symmetric functionals, Eletr. J. Diff. Eq, issue.3, pp.1-14, 1996.

O. Lopes, Nonlocal variational problems arising in long wave propagation, ESAIM Control Optim. Calc. Var, vol.5, pp.501-528, 2000.

M. Mari?, On the existence, regularity and decay of solitary waves to a generalized Benjamin-Ono equation, Nonlinear Analysis, vol.51, pp.1073-1085, 2002.

O. Sanchez and J. Soler, Long-time dynamics of the Schrödinger-Poisson-Slater system, J. Statistical Phys, vol.114, issue.2, pp.179-204, 2004.

E. Stein, Singular integrals and differentiability properties of functions, 1970.

E. M. Stein and G. Weiss, Fourier Analysis on Euclidean Spaces, 1971.

W. Troy, Symmetry properties in systems of semilinear elliptic equations, J. Differential Equations, vol.42, issue.3, pp.400-413, 1981.

M. Willem and . Minimax-theorems, Progr. Nonlinear Differential Equations Appl, vol.24, 1996.

I. V. Barashenkov, A. D. Gocheva, V. G. Makhankov, and I. V. Puzynin, Stability of soliton-like bubbles, Phys. D, vol.34, pp.240-254, 1989.

I. V. Barashenkov and V. G. Makhankov, Soliton-like "bubbles" in a system of interacting bosons, Phys. Lett. A, vol.128, pp.52-56, 1988.

H. Berestycki and P. Lions, Nonlinear scalar field equations, I. Existence of a ground state, Arch. Rational Mech. Anal, vol.82, pp.313-345, 1983.

J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, 1976.

F. Béthuel, P. Gravejat, and J. Saut, Travelling-waves for the GrossPitaevskii equation II

F. Béthuel, G. Orlandi, and D. Smets, Vortex rings for the Gross-Pitaevskii equation, J. Eur. Math. Soc. (JEMS), vol.6, pp.17-94, 2004.

F. Béthuel and J. Saut, Travelling-waves for the Gross-Pitaevskii equation I, Ann. Inst. H. Poincaré Phys. Théor, vol.70, pp.147-238, 1999.

H. Brézis, Analyse fonctionnelle, 1983.

H. Brézis, Semilinear equations in R N without condition at infinity, Appl. Math. Optim, vol.12, pp.271-282, 1984.

H. Brézis, J. Bourgain, and P. Mironescu, Lifting in Sobolev Spaces, Journal d'Analyse Mathématique, vol.80, pp.37-86, 2000.

H. Brézis and E. H. Lieb, Minimum Action Solutions for Some Vector Field Equations, Comm. Math. Phys, vol.96, pp.97-113, 1984.

D. Chiron, Travelling-waves for the Gross-Pitaevskii equation in dimension larger than two, Nonlinear Analysis, vol.58, pp.175-204, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00876577

A. Farina, Finite-energy solutions, quantization effects and Liouville-type results for a variant of the Ginzburg-Landau systems in R k, Diff. Int. Eq, vol.11, issue.6, pp.875-893, 1998.

A. Farina, From Ginzburg-Landau to Gross-Pitaevskii, Monatsh. Math, vol.139, pp.265-269, 2003.

P. Gérard, The Cauchy Problem for the Gross-Pitaevskii Equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.23, issue.5, pp.765-779, 2006.

J. Grant and P. H. Roberts, Motions in a Bose condensate III. The structure and effective masses of charged and uncharged impurities, J. Phys. A: Math., Nucl. Gen, vol.7, pp.260-279, 1974.

P. Gravejat, A non-existence result for supersonic travelling-waves in the Gross-Pitaevskii equation, Comm. Math. Phys, vol.243, issue.1, pp.93-103, 2003.

P. Gravejat, Limit at infinity and non-existence results for sonic travellingwaves in the Gross-Pitaevskii equation, Diff. Int. Eq, vol.17, issue.11, pp.1213-1232, 2004.

E. P. Gross, Hydrodynamics of a superfluid condensate, J. Math. Phys, vol.4, issue.2, pp.195-207, 1963.

L. Hörmander, The Analysis of Linear Partial Differential Operators, vol.1, 1983.

C. A. Jones and P. H. Roberts, Motions in a Bose condensate IV, Axisymmetric solitary waves, J. Phys A: Math. Gen, vol.15, pp.2599-2619, 1982.

C. A. Jones, S. J. Putterman, and P. H. Roberts, Motions in a Bose condensate V. Stability of wave solutions of nonlinear Schrödinger equations in two and three dimensions, J. Phys A: Math. Gen, vol.19, pp.2991-3011, 1986.

T. Kato, Schrödinger operators with singular potentials, Israel J. Math, vol.13, pp.135-148, 1972.

P. I. Lizorkin, On multipliers of Fourier integrals in the spaces L p,?, Proc. Steklov Inst. Math, vol.89, pp.269-290, 1967.

M. Mari?, Existence of nonstationary bubbles in higher dimensions, J. Math. Pures Appl, vol.81, pp.1207-1239, 2002.

M. Mari?, Global branches of travelling-waves to a Gross-Pitaevskii-Schrödinger system in one dimension, SIAM J. Math. Anal, vol.37, issue.5, pp.1535-1559, 2006.

E. Stein, Singular integrals and differentiability properties of functions, 1970.

L. Almeida and F. Béthuel, Topological methods for the Ginzburg-Landau equations, J. Math. Pures Appl, vol.77, pp.1-49, 1998.

I. V. Barashenkov, A. D. Gocheva, V. G. Makhankov, and I. V. Puzynin, Stability of soliton-like bubbles, Physica D, vol.34, pp.240-254, 1989.

I. V. Barashenkov and V. G. Makhankov, Soliton-like "bubbles" in a system of interacting bosons, Phys. Lett. A, vol.128, pp.52-56, 1988.

N. Berloff, Quantised vortices, travelling coherent structures and superfluid turbulence, in Stationary and time dependent Gross-Pitaevskii equations, Contemp. Math, vol.473, pp.26-54, 2008.

F. Béthuel, P. Gravejat, and J. Saut, Travelling-waves for the Gross-Pitaevskii equation II, Comm. Math. Phys, vol.285, pp.567-651, 2009.

F. Béthuel, G. Orlandi, and D. Smets, Vortex rings for the Gross-Pitaevskii equation, J. Eur. Math. Soc. (JEMS), vol.6, pp.17-94, 2004.

F. Béthuel and J. Saut, Travelling-waves for the Gross-Pitaevskii equation I, Ann. Inst. H. Poincaré Phys. Théor, vol.70, pp.147-238, 1999.

H. Brézis, Analyse fonctionnelle, 1983.

H. Brézis, J. Bourgain, and P. Mironescu, Lifting in Sobolev Spaces, Journal d'Analyse Mathématique, vol.80, pp.37-86, 2000.

H. Brézis and E. H. Lieb, Minimum Action Solutions for Some Vector Field Equations, Comm. Math. Phys, vol.96, pp.97-113, 1984.

D. Chiron, Travelling-waves for the Gross-Pitaevskii equation in dimension larger than two, Nonlinear Analysis, vol.58, pp.175-204, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00876577

C. Coste, Nonlinear Schrödinger equation and superfluid hydrodynamics, Eur. Phys. J. B, vol.1, pp.245-253, 1998.

A. De-bouard, Instability of stationary bubbles, SIAM J. Math. Anal, vol.26, issue.3, pp.566-582, 1995.

L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, 1992.

A. Farina, Finite-energy solutions, quantization effects and Liouville-type results for a variant of the Ginzburg-Landau systems in R k, Diff. Int. Eq, vol.11, issue.6, pp.875-893, 1998.

A. Farina, From Ginzburg-Landau to Gross-Pitaevskii, Monatsh. Math, vol.139, pp.265-269, 2003.

P. Gérard, The Cauchy Problem for the Gross-Pitaevskii Equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.23, issue.5, pp.765-779, 2006.

P. Gérard, The Gross-Pitaevskii equation in the energy space, Stationary and time dependent Gross-Pitaevskii equations, vol.473, pp.129-148, 2008.

D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol.3, 2001.

J. Grant and P. H. Roberts, Motions in a Bose condensate III. The structure and effective masses of charged and uncharged impurities, J. Phys. A: Math., Nucl. Gen, vol.7, pp.260-279, 1974.

P. Gravejat, A nonexistence result for supersonic travelling waves in the GrossPitaevskii equation, Comm. Math. Phys, vol.243, issue.1, pp.93-103, 2003.

E. P. Gross, Hydrodynamics of a superfluid condensate, J. Math. Phys, vol.4, issue.2, pp.195-207, 1963.

S. V. Iordanskii and A. V. Smirnov, Three-dimensional solitons in He II, JETP Lett, vol.27, issue.10, pp.535-538, 1978.

C. A. Jones and P. H. Roberts, Motions in a Bose condensate IV, Axisymmetric solitary waves, J. Phys A: Math. Gen, vol.15, pp.2599-2619, 1982.

C. A. Jones, S. J. Putterman, and P. H. Roberts, Motions in a Bose condensate V. Stability of wave solutions of nonlinear Schrödinger equations in two and three dimensions, J. Phys A: Math. Gen, vol.19, pp.2991-3011, 1986.

O. Kavian, Introductionà la théorie des points critiques et applications aux problèmes elliptiques, 1993.

Y. S. Kivshar and B. Luther-davies, Dark optical solitons: physics and applications, Phys. Rep, vol.298, pp.81-197, 1998.

Y. S. Kivshar, D. E. Pelinovsky, and Y. A. Stepanyants, Self-focusing of plane dark solitons in nonlinear defocusing media, Phys. Rev. E, vol.51, issue.5, pp.5016-5026, 1995.

E. H. Lieb, On the lowest eigenvalue of the Laplacian for the intersection of two domains, Invent. Math, vol.74, pp.441-448, 1983.

P. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case, part I, Ann. Inst. H. Poincaré, Anal. non linéaire, vol.1, pp.109-145, 1984.

M. Mari?, Existence of nonstationary bubbles in higher dimensions, J. Math. Pures Appl, vol.81, pp.1207-1239, 2002.

M. Mari?, On the symmetry of minimizers, Arch. Rational Mech. Anal

M. Mari?, Nonexistence of supersonic traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity, SIAM J. Math. Anal, vol.40, issue.3, pp.1076-1103, 2008.

E. M. Stein, Singular integrals and differentiability properties of functions, 1970.

E. Tarquini, A lower bound on the energy of travelling waves of fixed speed for the Gross-Pitaevskii equation, Monatsh. Math, vol.151, issue.4, pp.333-339, 2007.

M. Willem, Minimax Theorems, p.54, 1996.

, Global branches of travelling waves to a Gross-Pitaevskii-Schrödinger system in one dimension M, vol.37, pp.1535-1559, 2006.

, Global branches of travelling-waves to a Gross-Pitaevskii-Schrödinger system in one dimension Mihai MARI?, vol.6623, 25030.

F. Bethuel, G. Orlandi, and D. Smets, Vortex rings for the Gross-Pitaevskii equation, J. Eur. Math. Soc. (JEMS), vol.6, issue.1, pp.17-94, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00020106

F. Bethuel and J. Saut, Travelling waves for the Gross-Pitaevskii equation I, Ann. Inst. Henri Poincaré, vol.70, issue.2, pp.147-238, 1999.

D. Chiron, Étude mathématique de modèles issus de la physique de la matière condensée, 2004.

M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal, vol.8, pp.321-340, 1971.

J. Grant and P. H. Roberts, Motions in a Bose condensate III. The structure and effective masses of charged and uncharged impurities, J. Phys. A: Math., Nucl. Gen, vol.7, issue.2, pp.260-279, 1974.

M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, 1964.

M. Mari?, Stationary solutions to a nonlinear Schrödinger equation with potential in one dimension, Proc. Royal Soc. Edinburgh, vol.133, pp.409-437, 2003.

K. Mcleod, Uniqueness of positive radial solutions of ?u + f (u) = 0 in R N, Trans. Amer. Math. Soc, vol.II, issue.2, pp.495-505, 1993.

J. Pejsachowicz and P. J. Rabier, Degree theory for C 1 Fredholm mappings of index 0, Journal d'Analyse Mathématique, vol.76, pp.289-319, 1998.

P. J. Rabier and C. A. Stuart, Global bifurcation for quasilinear elliptic equations on R N, Math. Z, vol.237, pp.85-124, 2001.

P. J. Rabier and C. A. Stuart, Fredholm and Properness Properties of Quasilinear Elliptic Operators on R N, Math. Nachr, vol.231, pp.129-168, 2001.

P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal, vol.7, pp.487-513, 1971.

M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol.IV, 1978.