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
Positivity Properties and Stability of Solitary-Wave Solutions of Model Equations For Long Waves, Communications in Partial Differential Equations, vol.17, issue.1, pp.1-22, 1992. ,
DOI : 10.1080/03605309208820831
Stability Criterion for Dark Solitons, Physical Review Letters, vol.77, issue.7, pp.1193-1197, 1996. ,
DOI : 10.1103/PhysRevLett.77.1193
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
Propagating phase boundaries and capillary fluids. Lecture notes of CIRM summer school Mathematical Fluid Dynamics, 2010. ,
URL : https://hal.archives-ouvertes.fr/cel-00582329
Spectral transverse instability of solitary waves in Korteweg fluids, Journal of Mathematical Analysis and Applications, vol.361, issue.2, pp.338-357, 2010. ,
DOI : 10.1016/j.jmaa.2009.07.023
Structure of Korteweg models and stability of diffuse interfaces. Interfaces Free Bound, pp.371-414, 2005. ,
Instabilité desétatsdesétats stationnaires dans leséquationsleséquations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sci. Paris Sér. I Math, vol.293, issue.9, pp.489-492, 1981. ,
On the linear wave regime of the Gross-Pitaevskii equation, Journal d'Analyse Math??matique, vol.15, issue.1, pp.297-338, 2010. ,
DOI : 10.1007/s11854-010-0008-1
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
Linear Instability of Solitary Wave Solutions of the Kawahara Equation and Its Generalizations, SIAM Journal on Mathematical Analysis, vol.33, issue.6, pp.1356-1378, 2002. ,
DOI : 10.1137/S0036141099361494
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 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
Travelling waves for the Nonlinear Schrödinger Equation with general nonlinearity in dimension two ,
Nonlinear Instability of a Critical Traveling Wave in the Generalized Korteweg???de Vries Equation, SIAM Journal on Mathematical Analysis, vol.39, issue.1, pp.1-33, 2007. ,
DOI : 10.1137/060651501
Purely nonlinear instability of standing waves with minimal energy, Communications on Pure and Applied Mathematics, vol.16, issue.11, pp.1565-1607, 2003. ,
DOI : 10.1002/cpa.10104
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
Stability of dark screening solitons in photorefractive media, Theoretical and Mathematical Physics, vol.16, issue.1, pp.917-924, 2009. ,
DOI : 10.1007/s11232-009-0081-8
Dark solitons in discrete lattices: Saturable versus cubic nonlinearities, Physical Review E, vol.75, issue.6, p.66608, 2007. ,
DOI : 10.1103/PhysRevE.75.066608
Schrödinger group on Zhidkov spaces, Adv. Differential Equations, vol.9, issue.56, pp.509-538, 2004. ,
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 gap lemma and geometric criteria for instability of viscous shock profiles, Communications on Pure and Applied Mathematics, vol.51, issue.7, pp.797-855, 1998. ,
DOI : 10.1002/(SICI)1097-0312(199807)51:7<797::AID-CPA3>3.0.CO;2-1
Spectral theory for contraction semigroups on Hilbert space, Transactions of the American Mathematical Society, vol.236, pp.385-394, 1978. ,
DOI : 10.1090/S0002-9947-1978-0461206-1
Nonlinear instability of linearly unstable standing waves for nonlinear Schr??dinger equations, Journal of the Mathematical Society of Japan, vol.64, issue.2, pp.533-548, 2012. ,
DOI : 10.2969/jmsj/06420533
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
A spectral mapping theorem and invariant manifolds for nonlinear Schrödinger equations, Indiana Univ. Math. J, vol.49, pp.221-243, 2000. ,
On the theory of superfluidity, Sov. Phys. JETP, vol.34, p.1240, 1958. ,
On the nonlinear instability of Euler and Prandtl equations, Communications on Pure and Applied Mathematics, vol.80, issue.9, pp.1067-1091, 2000. ,
DOI : 10.1002/1097-0312(200009)53:9<1067::AID-CPA1>3.0.CO;2-Q
Linearized instability for nonlinear schr??dinger and klein-gordon equations, Communications on Pure and Applied Mathematics, vol.16, issue.6, pp.747-774, 1988. ,
DOI : 10.1002/cpa.3160410602
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
Stability theory of solitary waves in the presence of symmetry, II, Journal of Functional Analysis, vol.94, issue.2, pp.94-308, 1990. ,
DOI : 10.1016/0022-1236(90)90016-E
Hydrodynamics of a Superfluid Condensate, Journal of Mathematical Physics, vol.4, issue.2, pp.195-207, 1963. ,
DOI : 10.1063/1.1703944
Stability theory for solitary-wave solutions of scalar field equations, Communications in Mathematical Physics, vol.55, issue.3, pp.351-361, 1982. ,
DOI : 10.1007/BF01208719
Introduction to spectral theory. With applications to Schrödinger operators, Applied Mathematical Sciences, vol.113, 1996. ,
Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations. Phys, pp.3-58, 1998. ,
Perturbation Theory for Linear Operators, 1976. ,
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
Perturbation-induced dynamics of dark solitons, Physical Review E, vol.49, issue.2, pp.1657-1670, 1994. ,
DOI : 10.1103/PhysRevE.49.1657
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 travelling solitonic bubbles, Adv. Differential Equations, vol.7, issue.8, pp.897-918, 2002. ,
Instability of nonlinear dispersive solitary waves, Journal of Functional Analysis, vol.255, issue.5, pp.1191-1224, 2008. ,
DOI : 10.1016/j.jfa.2008.06.003
A linearized instability result for solitary waves, Discrete and Continuous Dynamical Systems, vol.8, issue.1, pp.115-119, 2002. ,
DOI : 10.3934/dcds.2002.8.115
Stability of bound states of Hamiltonian PDE's in the degenerate cases, pp.511-528, 2012. ,
Stability and instability of standing waves for 1-dimensional nonlinear Schr??dinger equation with multiple-power nonlinearity, Kodai Mathematical Journal, vol.31, issue.2, pp.263-271, 2008. ,
DOI : 10.2996/kmj/1214442798
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
Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity: existence, stability and dynamics. Phys, pp.551-567, 2008. ,
A remark on linearly unstable standing wave solutions to NLS. Nonlinear Anal, pp.657-676, 2006. ,
Instability of bound states for abstract nonlinear Schr??dinger equations, Journal of Functional Analysis, vol.261, issue.1, pp.90-110, 2011. ,
DOI : 10.1016/j.jfa.2011.03.010
Semitopological solitons in planar ferromagnets, Nonlinearity, vol.12, issue.2, pp.285-302, 1999. ,
DOI : 10.1088/0951-7715/12/2/008
Eigenvalues, and Instabilities of Solitary Waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.340, issue.1656, pp.1656-1703, 1992. ,
DOI : 10.1098/rsta.1992.0055
Dark solitons in external potentials, Zeitschrift f??r angewandte Mathematik und Physik, vol.59, issue.4, pp.559-599, 2008. ,
DOI : 10.1007/s00033-007-6120-0
On the Spectrum of C 0 -Semigroups, Transactions of the American Mathematical Society, vol.284, issue.2, pp.847-857, 1984. ,
DOI : 10.2307/1999112
Nonlinear Schrödinger equation as a model of superfluid helium Quantized Vortex Dynamics and Superfluid Turbulence, Lecture Notes in Physics, vol.571, 2001. ,
Transverse nonlinear instability for two-dimensional dispersive models, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.2, pp.477-496, 2009. ,
DOI : 10.1016/j.anihpc.2007.09.006
URL : https://hal.archives-ouvertes.fr/hal-00458107
Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's, Journal de Math??matiques Pures et Appliqu??es, vol.90, issue.6, pp.550-590, 2008. ,
DOI : 10.1016/j.matpur.2008.07.004
Stability of travelling waves. Handbook of dynamical systems, pp.983-1055, 2002. ,
Spectral condition for instability. Nonlinear PDE's, dynamics and continuum physics, Contemp. Math. Amer. Math. Soc, vol.189, issue.255, 1998. ,
Instability of nonlinear bound states, Communications in Mathematical Physics, vol.96, issue.2, pp.173-190, 1985. ,
DOI : 10.1007/BF01212446
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
Lyapunov stability of ground states of nonlinear dispersive evolution equations, Communications on Pure and Applied Mathematics, vol.38, issue.1, pp.51-67, 1986. ,
DOI : 10.1002/cpa.3160390103
Korteweg-de-Vries and Nonlinear Schrödinger Equations: Qualitative Theory, Lecture Notes in Mathematics, vol.1756, 2001. ,
A Sharp Stability Criterion for Soliton-Type Propagating Phase Boundaries in Korteweg's Model, Zeitschrift f??r Analysis und ihre Anwendungen, vol.27, issue.1, pp.11-30, 2008. ,
DOI : 10.4171/ZAA/1341