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
Stability Criterion for Dark Solitons, Physical Review Letters, vol.77, issue.7, pp.1193-1197, 1996. ,
DOI : 10.1103/PhysRevLett.77.1193
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
Stability and evolution of the quiescent and travelling solitonic bubbles, Physica D: Nonlinear Phenomena, vol.69, issue.1-2, pp.1-2, 1993. ,
DOI : 10.1016/0167-2789(93)90184-3
Existence and properties of travelling waves for the Gross-Pitaevskii equation, Contemp. Math, vol.473, pp.55-103, 2008. ,
DOI : 10.1090/conm/473/09224
Orbital stability of the black soliton for the Gross-Pitaevskii equation, Indiana University Mathematics Journal, vol.57, issue.6, pp.2611-2642, 2008. ,
DOI : 10.1512/iumj.2008.57.3632
Stability criterion in imperfect Bose gas Fiz, Nizk. Temp, vol.15, pp.511-513, 1989. ,
Stability and Instability of Solitary Waves of Korteweg-de Vries Type, Proc. R. Soc. Lond. A, pp.411-395, 1987. ,
DOI : 10.1098/rspa.1987.0073
Traveling waves for the Nonlinear Schrödinger Equation with general nonlinearity in dimension two ,
Instability of Stationary Bubbles, SIAM Journal on Mathematical Analysis, vol.26, issue.3, pp.566-582, 1995. ,
DOI : 10.1137/S0036141092237029
The black solitons of one-dimensional NLS equations, Nonlinearity, vol.20, issue.2, pp.461-496, 2007. ,
DOI : 10.1088/0951-7715/20/2/010
The Cauchy problem for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity, Comm. Partial Differential Equations, vol.33, issue.4, pp.6-729, 2008. ,
The Gross-Pitaevskii equation in the energy space, Contemp. Math, vol.473, pp.129-148, 2008. ,
DOI : 10.1090/conm/473/09226
Orbital stability of traveling waves for the one-dimensional Gross???Pitaevskii equation, Journal de Math??matiques Pures et Appliqu??es, vol.91, issue.2, pp.178-210, 2009. ,
DOI : 10.1016/j.matpur.2008.09.009
On the theory of superfluidity, Sov. Phys. JETP, vol.34, p.1240, 1958. ,
Stability theory of solitary waves in the presence of symmetry, I, Journal of Functional Analysis, vol.74, issue.1, pp.160-197, 1987. ,
DOI : 10.1016/0022-1236(87)90044-9
Hydrodynamics of a Superfluid Condensate, Journal of Mathematical Physics, vol.4, issue.2, pp.195-207, 1963. ,
DOI : 10.1063/1.1703944
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
Modulational instabilities and dark solitons in a generalized nonlinear Schrödinger equation, Phys. Scr, pp.47-679, 1993. ,
Instabilities of dark solitons, Optics Letters, vol.20, issue.14, pp.14-1527, 1995. ,
DOI : 10.1364/OL.20.001527
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
Low-Dimensional Bose Liquids: Beyond the Gross-Pitaevskii Approximation, Physical Review Letters, vol.85, issue.6, pp.1146-1149, 2000. ,
DOI : 10.1103/PhysRevLett.85.1146
Stability and instability of traveling solitonic bubbles, Adv. Differential Equations, vol.7, issue.8, pp.897-918, 2002. ,
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
Instability of solitons for the critical generalized Korteweg???de Vries equation, Geometric and Functional Analysis, vol.11, issue.1, pp.74-123, 2001. ,
DOI : 10.1007/PL00001673
URL : https://hal.archives-ouvertes.fr/hal-00189836
Blow up in finite time and dynamics of blow up solutions for the L 2 -critical generalized KdV equation, Journal of the American Mathematical Society, vol.15, issue.03, pp.617-664, 2002. ,
DOI : 10.1090/S0894-0347-02-00392-2
URL : https://hal.archives-ouvertes.fr/hal-00107235
Nonlinear Schrödinger equation as a model of superfluid helium Quantized Vortex Dynamics and Superfluid Turbulence, Lecture Notes in Physics, vol.571, 2001. ,
Synopsis, Proc. Roy. Soc. Edinburgh A, pp.114-195, 1990. ,
DOI : 10.1007/BF01212446
Nonlinear waves in the Pitaevskii-Gross equation, Journal of Low Temperature Physics, vol.25, issue.4, pp.441-457, 1971. ,
DOI : 10.1007/BF00628744
Multi-scale expansions in the theory of systems integrable by the inverse scattering transform, Physica D: Nonlinear Phenomena, vol.18, issue.1-3, pp.455-463, 1986. ,
DOI : 10.1016/0167-2789(86)90214-9
Korteweg-de-Vries and Nonlinear Schrödinger Equations: Qualitative Theory, Lecture Notes in Mathematics, vol.1756, 2001. ,