The inverse spectral problem for Hankel operators of nite rank, Russian. English, Russian summary) Zap. Nauchn. Sem. S.-Peterburg. Otdel ,
The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems, Studies in Applied Mathematics, vol.34, issue.12, p.249315, 1974. ,
DOI : 10.1002/sapm1974534249
On the renormalization group approach to perturbation theory for PDEs, p.10071021, 2010. ,
Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, vol.60, 1989. ,
Ergodic Problems of Classical Mechanics, 1968. ,
High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations, American Journal of Mathematics, vol.121, issue.1, p.131175, 1999. ,
DOI : 10.1353/ajm.1999.0001
Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg, (French. English summary) [Besov spaces and generalized Strichartz estimates on the Heisenberg group, J. Anal. Math, pp.82-93118, 2000. ,
Mitropol'skii Asymptotic Methods in the Theory of Nonlinear Oscillations, 1958. ,
On the Cauchy problem for periodic KdV-type equations, Proceedings of the Conference in Honor of Jean-Pierre Kahane, p.1786, 1993. ,
Aspects of long time behaviour of solutions of nonlinear Hamiltonian evolution equations, Geom. Funct. Anal, vol.5, issue.2, p.105140, 1995. ,
On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE, Internat. Math. Res. Notices, issue.6, p.277304, 1996. ,
Remarks on stability and diusion in high-dimensional Hamiltonian systems and partial dierential equations, Ergodic Theory Dynam, Systems, vol.24, issue.5, p.13311357, 2004. ,
Nonlinear Schrödinger Equations, Hyperbolic equations and frequency interactions (Park City, Math. Soc, 1995. ,
Soliton dynamics in a potential, Mathematical Research Letters, vol.7, issue.3, p.32942, 2000. ,
DOI : 10.4310/MRL.2000.v7.n3.a7
An instability property of the nonlinear Schrödinger equation on S d, pp.323-335, 2002. ,
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, Amer, J. Math, vol.126, p.569605, 2004. ,
Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces, Invent. Math, vol.159, p.187223, 2005. ,
Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys, vol.85, issue.4, p.549561, 1982. ,
Renormalization Group Theory for Global Asymptotic Analysis, Physical Review Letters, vol.73, issue.10, p.13111315, 1994. ,
DOI : 10.1103/PhysRevLett.73.1311
Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory, Physical Review E, vol.54, issue.1, p.376394, 1996. ,
DOI : 10.1103/PhysRevE.54.376
Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R 3, Ann. of Math, vol.167, issue.2 3, p.767865, 2008. ,
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation, Invent. Math, vol.181, issue.1, p.39113, 2010. ,
Inverse scattering on the line, Communications on Pure and Applied Mathematics, vol.45, issue.2, p.121251, 1979. ,
DOI : 10.1002/cpa.3160320202
Analysis of a renormalization group method and normal form theory for perturbed ordinary dierential equations, Physica D, pp.237-10291052, 2008. ,
On global action-angle coordinates, Communications on Pure and Applied Mathematics, vol.6, issue.3, p.687706, 1980. ,
DOI : 10.1002/cpa.3160330602
The emergence of solitons of the korteweg-de vries equation from arbitrary initial conditions, Mathematical Methods in the Applied Sciences, vol.59, issue.1, p.116, 1983. ,
DOI : 10.1002/mma.1670050108
The Liouville??Arnold??Nekhoroshev theorem for non-compact invariant manifolds, Journal of Physics A: Mathematical and General, vol.36, issue.7, p.107, 2003. ,
DOI : 10.1088/0305-4470/36/7/102
Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds, Journal of Mathematical Physics, vol.48, issue.3, p.32901, 2007. ,
DOI : 10.1063/1.2713079
Solitary Wave Dynamics in an External Potential, Communications in Mathematical Physics, vol.16, issue.3, pp.250-61342, 2004. ,
DOI : 10.1007/s00220-004-1128-1
Long time motion of NLS solitary waves in a conning potential, Annales Henri Poincaré, vol.7, p.621660, 2006. ,
On the point-particle (Newtonian) limit of the nonlinear Hartree equation, Comm. Math. Phys, pp.225-22374, 2002. ,
Description du défaut de compacité de l'injection de Sobolev, French) ESAIM : Control, Optimisation and Calculus of Variation, p.213233, 1998. ,
The cubic Szegö equation, Annales Scientiques de l'Ecole Normale Supérieure, pp.43-761810, 2010. ,
Invariant tori for the cubic Szegö equation ,
Eective integrable dynamics for some nonlinear wave equation, 2011. ,
Space-time resonances, Journ??es ??quations aux d??riv??es partielles ,
DOI : 10.5802/jedp.65
URL : https://hal.archives-ouvertes.fr/hal-00873086
Global existence for coupled Klein-Gordon equations with dierent speeds ,
Global solutions for the gravity water waves equation in dimension 3, Comptes Rendus Mathematique, vol.347, issue.15-16, pp.1516-897902, 2009. ,
DOI : 10.1016/j.crma.2009.05.005
Global solutions for 3D quadratic Schrödinger equations, Int. Math. Res. Not, issue.3, p.414432, 2009. ,
Resonant dynamics for the quintic nonlinear Schrödinger equation, 2011. ,
SCATTERING THEORY FOR THE GROSS???PITAEVSKII EQUATION IN THREE DIMENSIONS, Communications in Contemporary Mathematics, vol.11, issue.04, p.707, 2009. ,
DOI : 10.1142/S0219199709003491
Global and dynamical aspects of nonlinear Schrödinger equations on compact manifolds, 2011. ,
Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett, vol.27, p.11921194, 1971. ,
Remarks on the blow-up for the L 2 -critical nonlinear Schrödinger equations, SIAM J. Math. Anal, vol.38, issue.4, p.10351047, 2006. ,
Slow soliton interaction with delta impurities, J. Mod. Dyn, vol.1, issue.4, p.689718, 2007. ,
Soliton Interaction with Slowly Varying Potentials, International Mathematics Research Notices, vol.36, issue.10, p.pp, 2008. ,
DOI : 10.1093/imrn/rnn026
Eective dynamics of double solitons for perturbed mKdV, preprint arXiv, pp.912-5122 ,
The Analysis of Linear and Partial Dierential Operators I, Distribution Theory and Fourier Analysis, second edition, Classics in Mathematics, 2003. ,
On the defect of compactness for the Strichartz estimates of the Schrödinger equations, J. Dierential Equations, vol.175, p.353392, 2001. ,
Semiclassical limit of a class of Schrödinger equations with potential, Comm. Partial Dierential Equations, vol.27, issue.3, pp.4-693704, 2002. ,
Semiclassical limit for nonlinear Schrödinger equation with potential. II, Asymptot, Anal, vol.47, issue.34, p.171186, 2006. ,
Oscillations in space-periodic nonlinear Schrödinger equations ,
Translation invariant spaces, Acta Mathematica, vol.101, issue.3-4, p.163178, 1959. ,
DOI : 10.1007/BF02559553
Integrals of nonlinear equations of evolution and solitary waves, Communications on Pure and Applied Mathematics, vol.15, issue.5, p.467490, 1968. ,
DOI : 10.1002/cpa.3160210503
Linear algebra, Pure and Applied Mathematics, 1997. ,
The concentration-compactness principle in the calculus of variations . The locally compact case. I, Ann, Inst. H. Poincaré Anal. Non Linéaire, vol.1, issue.2, p.109145, 1984. ,
The concentration-compactness principle in the calculus of variations . The locally compact case. II, Ann, Inst. H. Poincaré Anal. Non Linéaire, vol.1, issue.4, p.223283, 1984. ,
Theory of Solitons. The Inverse Scattering Method, Translated from the Russian, Contemporary Soviet Mathematics. Consultants Bureau, 1984. ,
Generic Hamiltonian Systems are Neither Integrable nor Ergodic, Memoirs of the A, M.S, vol.144, 1974. ,
Description of two soliton collision for the quartic gKdV equation, Annals of Mathematics, vol.174, issue.2 ,
DOI : 10.4007/annals.2011.174.2.2
URL : https://hal.archives-ouvertes.fr/hal-00690291
The inverse spectral problem for selfadjoint Hankel operators, Acta Math, p.241309, 1995. ,
Compactness at blowup time for L2 solutions of the critical nonlinear Schrödinger equations in 2D, Int. Math. Res. Not, vol.8, p.399425, 1998. ,
Renormalization group method. Applications to Navier- Stokes equation, Discret. Continuous Dyn. Syst, vol.6, 2000. ,
Renormalization Group Method. Applications to Partial Differential Equations, J. Dyn. Dier. Equ, vol.13, p.275321, 2001. ,
Functions and Systems : An Easy Reading, Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, 2002. ,
Theory of Solitons : The Inverse Scattering Method, p.Nauka, 1980. ,
A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations, Nonlinear Anal, pp.14-765769, 1990. ,
Hankel Operators and Their Applications, 2003. ,
DOI : 10.1007/978-0-387-21681-2
A remark on soliton-potential interactions for nonlinear Schrödinger equations, Math. Res. Lett, vol.16, issue.3, p.477486, 2009. ,
Renormalization group method applied to the primitive equations, Journal of Differential Equations, vol.208, issue.1, p.215257, 2005. ,
DOI : 10.1016/j.jde.2003.10.011
Traveling waves for the cubic Szegö equation on the real line, arXiv :1001.4037v2 [math ,
Explicit formula for the solution of the Szegö equation on the real line and applications ,
Soliton interaction with small Toeplitz potentials for the cubic Szegö equation on the real line ,
First and second approximations for a non-linear wave equation ,
Les m??thodes nouvelles de la m??canique c??leste, Il Nuovo Cimento, vol.10, issue.1, 1957. ,
DOI : 10.1007/BF02742713
Real and Complex Analysis, 1980. ,
Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4, Amer. J. Math, vol.129, issue.1, p.160, 2007. ,
Space-time resonances, Quarterly of Applied Mathematics, vol.68, issue.1, p.161167, 2010. ,
DOI : 10.1090/S0033-569X-09-01175-3
Why are solitons stable ?, Bulletin (New Series) of the, p.133, 2009. ,
Averaging of dierential equations generating oscillations and an application to control, Special issue dedicated to the memory of Jacques-Louis Lions, Appl. Math. Optim, vol.46, issue.2, pp.3-313330, 2002. ,
Global well-posedness and scattering for the defocusing cubic NLS in four dimensions ,
On the solvability of a mixed problem for a nonlinear equation of Schrödinger type, Sov. math. Dokl, vol.29, p.281284, 1984. ,
An introduction to KAM theory Dynamical systems and probabilistic methods in partial dierential equations, Lectures in Appl. Math, vol.329, issue.31, 1994. ,
Nonlinear Schrödinger equations and sharp interpolation estimates, Com. Math. Phys, vol.87, p.567576, 1982. ,
DOI : 10.1007/bf01208265
Non-stationary ows of an ideal incompressible uid, Russian) Z. Vycisl. Mat. i Mat. Fiz, vol.3, p.10321066, 1963. ,
Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP, vol.34, p.6269, 1972. ,
On a certain renormalization group method, Journal of Mathematical Physics, vol.41, issue.5, 2000. ,
DOI : 10.1063/1.533307