메뉴 건너뛰기




Volumn 203, Issue 2, 2003, Pages 453-493

On the role of quadratic oscillations in nonlinear Schrödinger equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0141503425     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(03)00212-X     Document Type: Article
Times cited : (7)

References (26)
  • 1
    • 0033074557 scopus 로고    scopus 로고
    • High frequency approximation of solutions to critical nonlinear wave equations
    • H. Bahouri, P. Gérard, High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math. 121 (1) (1999) 131-175.
    • (1999) Amer. J. Math. , vol.121 , Issue.1 , pp. 131-175
    • Bahouri, H.1    Gérard, P.2
  • 2
    • 0001605822 scopus 로고    scopus 로고
    • Geometric optics with caustic crossing for some nonlinear Schrödinger equations
    • R. Carles, Geometric optics with caustic crossing for some nonlinear Schrödinger equations, Indiana Univ. Math. J. 49 (2) (2000) 475-551.
    • (2000) Indiana Univ. Math. J. , vol.49 , Issue.2 , pp. 475-551
    • Carles, R.1
  • 3
    • 0036811041 scopus 로고    scopus 로고
    • Critical nonlinear Schrödinger equations with and without harmonic potential
    • R. Carles, Critical nonlinear Schrödinger equations with and without harmonic potential, Math. Mod. Meth. Appl. Sci. (M3AS) 12 (10) (2002) 1513-1523.
    • (2002) Math. Mod. Meth. Appl. Sci. (M3AS) , vol.12 , Issue.10 , pp. 1513-1523
    • Carles, R.1
  • 4
    • 0141814240 scopus 로고    scopus 로고
    • Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
    • R. Carles, Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (3) (2003) 501-542.
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , Issue.3 , pp. 501-542
    • Carles, R.1
  • 5
    • 0003197180 scopus 로고
    • An Introduction to Nonlinear Schrödinger Equations
    • Univ. Fed. Rio de Janeiro
    • T. Cazenave, An Introduction to Nonlinear Schrödinger Equations, Textos de Metodos Matématicos, Vol. 26, Univ. Fed. Rio de Janeiro, 1993.
    • (1993) Textos de Metodos Matématicos , vol.26
    • Cazenave, T.1
  • 6
    • 0002119090 scopus 로고
    • Rapidly decaying solutions of the nonlinear Schrödinger equation
    • T. Cazenave, F. Weissler, Rapidly decaying solutions of the nonlinear Schrödinger equation, Comm. Math. Phys. 147 (1992) 75-100.
    • (1992) Comm. Math. Phys. , vol.147 , pp. 75-100
    • Cazenave, T.1    Weissler, F.2
  • 7
    • 85031065442 scopus 로고    scopus 로고
    • Cours du collège de France, available at www.lkb.ens.fr/~laloe/PHYS/cours/college-de-france/
    • C. Cohen-Tannoudji, Cours du collège de France, 1998-99, available at www.lkb.ens.fr/~laloe/PHYS/cours/college-de-france/.
    • (1998)
    • Cohen-Tannoudji, C.1
  • 8
    • 0003495236 scopus 로고
    • International Series in Pure and Applied Physics, McGraw-Hill Publishing Company, Ltd., Maidenhead, Berksh
    • R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, International Series in Pure and Applied Physics, McGraw-Hill Publishing Company, Ltd., Maidenhead, Berksh, 1965, 365 pp.
    • (1965) Quantum Mechanics and Path Integrals , pp. 365
    • Feynman, R.P.1    Hibbs, A.R.2
  • 9
    • 0042904653 scopus 로고    scopus 로고
    • Profile decomposition for solutions of the Navier-Stokes equations
    • I. Gallagher, Profile decomposition for solutions of the Navier-Stokes equations, Bull. Soc. Math. France 129 (2) (2001) 285-316.
    • (2001) Bull. Soc. Math. France , vol.129 , Issue.2 , pp. 285-316
    • Gallagher, I.1
  • 10
    • 0030579045 scopus 로고    scopus 로고
    • Oscillations and concentration effects in semilinear dispersive wave equations
    • P. Gérard, Oscillations and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 141 (1) (1996) 60-98.
    • (1996) J. Funct. Anal. , vol.141 , Issue.1 , pp. 60-98
    • Gérard, P.1
  • 11
    • 84996132207 scopus 로고    scopus 로고
    • Description du défaut de compacité de l'injection de Sobolev
    • (electronic)
    • P. Gérard, Description du défaut de compacité de l'injection de Sobolev, ESAIM Control Optim. Calc. Var. 3 (1998) 213-233 (electronic).
    • (1998) ESAIM Control Optim. Calc. Var. , vol.3 , pp. 213-233
    • Gérard, P.1
  • 13
    • 0000555922 scopus 로고
    • Scattering theory in the energy space for a class of nonlinear Schrdsodinger equations
    • (9)
    • J. Ginibre, G. Velo, Scattering theory in the energy space for a class of nonlinear Schrdsodinger equations, J. Math. Pures Appl. (9) 64 (4) (1985) 363-401.
    • (1985) J. Math. Pures Appl. , vol.64 , Issue.4 , pp. 363-401
    • Ginibre, J.1    Velo, G.2
  • 14
    • 0001270512 scopus 로고
    • Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations
    • J. Ginibre, G. Velo, Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 43 (4) (1985) 399-442.
    • (1985) Ann. Inst. H. Poincaré Phys. Théor. , vol.43 , Issue.4 , pp. 399-442
    • Ginibre, J.1    Velo, G.2
  • 15
    • 2342560885 scopus 로고    scopus 로고
    • Caustics for dissipative semilinear oscillations
    • viii + 72
    • J.-L. Joly, G. Métivier, J. Rauch, Caustics for dissipative semilinear oscillations, Mem. Amer. Math. Soc. 144 (685) (2000) viii + 72.
    • (2000) Mem. Amer. Math. Soc. , vol.144 , Issue.685
    • Joly, J.-L.1    Métivier, G.2    Rauch, J.3
  • 16
    • 0035922239 scopus 로고    scopus 로고
    • On the defect of compactness for the Strichartz estimates of the Schrödinger equations
    • S. Keraani, On the defect of compactness for the Strichartz estimates of the Schrödinger equations, J. Differential Equations 175 (2) (2001) 353-392.
    • (2001) J. Differential Equations , vol.175 , Issue.2 , pp. 353-392
    • Keraani, S.1
  • 17
    • 0034246729 scopus 로고    scopus 로고
    • Low-dimensional Bose liquids: Beyond the Gross-Pitaevskii approximation
    • E.B. Kolomeisky, T.J. Newman, J.P. Straley, X. Qi, Low-dimensional Bose liquids: Beyond the Gross-Pitaevskii approximation, Phys. Rev. Lett. 85 (6) (2000) 1146-1149.
    • (2000) Phys. Rev. Lett. , vol.85 , Issue.6 , pp. 1146-1149
    • Kolomeisky, E.B.1    Newman, T.J.2    Straley, J.P.3    Qi, X.4
  • 18
    • 0001328731 scopus 로고    scopus 로고
    • Dispersive effects for nonlinear geometrical optics with rectification
    • D. Lannes, Dispersive effects for nonlinear geometrical optics with rectification, Asymptot. Anal. 18 (1-2) (1998) 111-146.
    • (1998) Asymptot. Anal. , vol.18 , Issue.1-2 , pp. 111-146
    • Lannes, D.1
  • 20
    • 84974001368 scopus 로고
    • Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
    • F. Merle, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power, Duke Math. J. 69 (2) (1993) 427-454.
    • (1993) Duke Math. J. , vol.69 , Issue.2 , pp. 427-454
    • Merle, F.1
  • 21
    • 1842709141 scopus 로고    scopus 로고
    • 2 solutions of the critical nonlinear Schrödinger equation in 2D
    • 2 solutions of the critical nonlinear Schrödinger equation in 2D, Internat. Math. Res. Notices (8) (1998) 399-425.
    • (1998) Internat. Math. Res. Notices , Issue.8 , pp. 399-425
    • Merle, F.1    Vega, L.2
  • 22
    • 0001304838 scopus 로고    scopus 로고
    • Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2
    • K. Nakanishi, Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2, J. Funct. Anal. 169 (1) (1999) 201-225.
    • (1999) J. Funct. Anal. , vol.169 , Issue.1 , pp. 201-225
    • Nakanishi, K.1
  • 23
    • 0035634148 scopus 로고    scopus 로고
    • Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations
    • (2)
    • K. Nakanishi, Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations, Tohoku Math. J. (2) 53 (2) (2001) 285-303.
    • (2001) Tohoku Math. J. , vol.53 , Issue.2 , pp. 285-303
    • Nakanishi, K.1
  • 24
    • 0013548254 scopus 로고
    • Weak limits of solutions to semilinear hyperbolic systems
    • M. Oberguggenberger, Weak limits of solutions to semilinear hyperbolic systems, Math. Ann. 274 (4) (1986) 599-607.
    • (1986) Math. Ann. , vol.274 , Issue.4 , pp. 599-607
    • Oberguggenberger, M.1
  • 25
    • 0003345993 scopus 로고
    • Partial Differential Equations
    • Springer, New York
    • J. Rauch, Partial Differential Equations, in: Graduate Texts in Mathematics, Vol. 128, Springer, New York, 1991.
    • (1991) Graduate Texts in Mathematics , vol.128
    • Rauch, J.1
  • 26
    • 0000695165 scopus 로고
    • Nonlinear superposition and absorption of delta waves in one space dimension
    • J. Rauch, M. Reed, Nonlinear superposition and absorption of delta waves in one space dimension, J. Funct. Anal. 73 (1) (1987) 152-178.
    • (1987) J. Funct. Anal. , vol.73 , Issue.1 , pp. 152-178
    • Rauch, J.1    Reed, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.