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Volumn 59, Issue 10, 2006, Pages 1379-1432

On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case

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EID: 33748300603     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20142     Document Type: Article
Times cited : (27)

References (18)
  • 1
    • 0242376125 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation as both a PDE and a dynamical system
    • North-Holland, Amsterdam
    • Cai, D.; McLaughlin, D. W.; McLaughlin, K. T. R. The nonlinear Schrödinger equation as both a PDE and a dynamical system. Handbook of dynamical systems, Vol. 2, 599-675. North-Holland, Amsterdam, 2002.
    • (2002) Handbook of Dynamical Systems, Vol. 2 , vol.2 , pp. 599-675
    • Cai, D.1    McLaughlin, D.W.2    McLaughlin, K.T.R.3
  • 2
    • 17944399485 scopus 로고    scopus 로고
    • A numerical study of the semi-classical limit of the focusing nonlinear Schrödinger equation
    • Ceniceros, H.; Tian, F.-R.; Ceniceros, H. D.; Tian, F.-R. A numerical study of the semi-classical limit of the focusing nonlinear Schrödinger equation. Phys. Lett. A 306 (2002), no. 1, 25-34.
    • (2002) Phys. Lett. A , vol.306 , Issue.1 , pp. 25-34
    • Ceniceros, H.1    Tian, F.-R.2    Ceniceros, H.D.3    Tian, F.-R.4
  • 3
    • 0033440723 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
    • Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X. Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 52 (1999), no. 11, 1335-1425.
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.11 , pp. 1335-1425
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, X.5
  • 5
    • 1842665167 scopus 로고    scopus 로고
    • New results in small dispersion KdV by an extension of the steepest descent method for Riemann-Hilbert problems
    • Deift, P.; Venakides, S.; Zhou, X. New results in small dispersion KdV by an extension of the steepest descent method for Riemann-Hilbert problems. Internat. Math. Res. Notices 1997, no. 6, 286-299.
    • Internat. Math. Res. Notices , vol.1997 , Issue.6 , pp. 286-299
    • Deift, P.1    Venakides, S.2    Zhou, X.3
  • 6
    • 0001525213 scopus 로고
    • A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
    • Deift, P.; Zhou, X. A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation. Ann. of Math. (2) 137 (1993), no. 2, 295-368.
    • (1993) Ann. of Math. (2) , vol.137 , Issue.2 , pp. 295-368
    • Deift, P.1    Zhou, X.2
  • 7
    • 84990647031 scopus 로고
    • Asymptotics for the Painlevé II equation
    • Deift, P.; Zhou, X. Asymptotics for the Painlevé II equation. Comm. Pure Appl. Math. 48 (1995), no. 3, 277-337.
    • (1995) Comm. Pure Appl. Math. , vol.48 , Issue.3 , pp. 277-337
    • Deift, P.1    Zhou, X.2
  • 8
    • 0002412295 scopus 로고
    • Geometry and modulation theory for the periodic nonlinear Schrödinger equation
    • The IMA Volumes in Mathematics and Its Applications, Springer, New York
    • Forest, M. G.; Lee, J. E. Geometry and modulation theory for the periodic nonlinear Schrödinger equation. Oscillation theory, computation, and methods of compensated compactness (Minneapolis, Minn., 1985), 35-69. The IMA Volumes in Mathematics and Its Applications, 2. Springer, New York, 1986.
    • (1986) Oscillation Theory, Computation, and Methods of Compensated Compactness (Minneapolis, Minn., 1985) , vol.2 , pp. 35-69
    • Forest, M.G.1    Lee, J.E.2
  • 11
    • 0002023137 scopus 로고    scopus 로고
    • On the semiclassical limit of the focusing nonlinear Schrödinger equation
    • Miller, P. D.; Kamvissis, S. On the semiclassical limit of the focusing nonlinear Schrödinger equation. Phys. Lett. A 247 (1998), no. 1-2, 75-86.
    • (1998) Phys. Lett. A , vol.247 , Issue.1-2 , pp. 75-86
    • Miller, P.D.1    Kamvissis, S.2
  • 12
    • 0039741902 scopus 로고    scopus 로고
    • The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases
    • Tovbis, A.; Venakides, S. The eigenvalue problem for the focusing nonlinear Schrödinger equation: new solvable cases. Phys. D 146 (2000), no. 1-4, 150-164.
    • (2000) Phys. D , vol.146 , Issue.1-4 , pp. 150-164
    • Tovbis, A.1    Venakides, S.2
  • 13
    • 2942535891 scopus 로고    scopus 로고
    • On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation
    • Tovbis, A.; Venakides, S.; Zhou, X. On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation. Comm. Pure Appl. Math. 57 (2004), no. 7, 877-985.
    • (2004) Comm. Pure Appl. Math. , vol.57 , Issue.7 , pp. 877-985
    • Tovbis, A.1    Venakides, S.2    Zhou, X.3
  • 14
    • 84990586440 scopus 로고
    • The Korteweg-de Vries equation with small dispersion: Higher order Lax-Levermore theory
    • Venakides, S. The Korteweg-de Vries equation with small dispersion: higher order Lax-Levermore theory. Comm. Pure Appl. Math. 43 (1990), no. 3, 335-361.
    • (1990) Comm. Pure Appl. Math. , vol.43 , Issue.3 , pp. 335-361
    • Venakides, S.1
  • 15
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • Zakharov, V. E.; Shabat, A. B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Soviet Physics JETP 34 (1972), no. 1, 62-69;
    • (1972) Soviet Physics JETP , vol.34 , Issue.1 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2
  • 16
    • 0000440099 scopus 로고
    • translated from Ž. Èksper. Teoret. Fiz. 61 (1971), no. 1, 118-134.
    • (1971) Ž. Èksper. Teoret. Fiz. , vol.61 , Issue.1 , pp. 118-134
  • 17
    • 0040113212 scopus 로고    scopus 로고
    • 2-Sobolev space bijectivity of the scattering and inverse scattering transforms
    • 2-Sobolev space bijectivity of the scattering and inverse scattering transforms. Comm. Pure Appl. Math. 51 (1998), no. 7, 697-731.
    • (1998) Comm. Pure Appl. Math. , vol.51 , Issue.7 , pp. 697-731
    • Zhou, X.1


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