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Volumn , Issue 154, 2003, Pages

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation

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EID: 85009055469     PISSN: 00662313     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Review
Times cited : (143)

References (47)
  • 2
    • 0001035750 scopus 로고    scopus 로고
    • Self-focusing and self-trapping of intense light beams in a nonlinear medium
    • [ASK66]
    • [ASK66] S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, "Self-focusing and self-trapping of intense light beams in a nonlinear medium," Sov. Phys. JETP, 23 (1996): 1025-1033.
    • (1996) Sov. Phys. JETP , vol.23 , pp. 1025-1033
    • Akhmanov, S.A.1    Sukhorukov, A.P.2    Khokhlov, R.V.3
  • 4
    • 0003225472 scopus 로고
    • Direct and Inverse Scattering on the Line
    • [BDT88], Amer. Math. Soc., Providence, R.I.
    • [BDT88] R. Beals, P. Deift, and C. Tomei, Direct and Inverse Scattering on the Line, Math. Surveys Monogr., 28, Amer. Math. Soc., Providence, R.I., 1988.
    • (1988) Math. Surveys Monogr. , vol.28
    • Beals, R.1    Deift, P.2    Tomei, C.3
  • 5
    • 0030263239 scopus 로고    scopus 로고
    • Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem
    • [B96]
    • [B96] J. C. Bronski, "Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem," Phys. D, 97 (1996): 376-397.
    • (1996) Phys. D , vol.97 , pp. 376-397
    • Bronski, J.C.1
  • 6
    • 4244193319 scopus 로고    scopus 로고
    • Spectral instability of the semiclassical Zakharov-Shabat eigenvalue problem
    • [B01]
    • [B01] _, "Spectral instability of the semiclassical Zakharov-Shabat eigenvalue problem," Phys. D, 152-153 (2001): 163-170.
    • (2001) Phys. D , vol.152-153 , pp. 163-170
  • 7
    • 0042781006 scopus 로고    scopus 로고
    • Numerical simulation of the semi-classical limit of the focusing nonlinear Schrödinger equation
    • [BK99]
    • [BK99] J. C. Bronski and J. N. Kutz, "Numerical simulation of the semi-classical limit of the focusing nonlinear Schrödinger equation," Phys. Lett. A, 254 (1999): 325-336.
    • (1999) Phys. Lett. A , vol.254 , pp. 325-336
    • Bronski, J.C.1    Kutz, J.N.2
  • 8
    • 57249083868 scopus 로고    scopus 로고
    • On the semiclassical limit for the focusing nonlinear Schrödinger equation: Sensitivity to analytic properties of the initial data
    • [CM02]
    • [CM02] S. R. Clarke and P. D. Miller, "On the semiclassical limit for the focusing nonlinear Schrödinger equation: sensitivity to analytic properties of the initial data," Proc. Roy. Soc. Lond. Ser. A, 458 (2002): 135-156.
    • (2002) Proc. Roy. Soc. Lond. Ser. A , vol.458 , pp. 135-156
    • Clarke, S.R.1    Miller, P.D.2
  • 9
    • 0003346458 scopus 로고    scopus 로고
    • Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
    • [D99], Courant Institute of Mathematical Sciences, New York
    • [D99] P. A. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics, Vol. 3, Courant Institute of Mathematical Sciences, New York, 1999.
    • (1999) Courant Lecture Notes in Mathematics , vol.3
    • Deift, P.A.1
  • 10
    • 0031493906 scopus 로고    scopus 로고
    • A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics
    • [DIZ97]
    • [DIZ97] P. Deift, A. Its, and X. Zhou, "A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics," Ann. of Math. (2), 146 (1997): 149-235.
    • (1997) Ann. of Math. (2) , vol.146 , pp. 149-235
    • Deift, P.1    Its, A.2    Zhou, X.3
  • 12
    • 0000743268 scopus 로고    scopus 로고
    • New results on the equilibrium measure for logarithmic potentials in the presence of an external field
    • [DKM98]
    • [DKM98] P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin, "New results on the equilibrium measure for logarithmic potentials in the presence of an external field," J. Approx. Theory, 95 (1998): 388-475.
    • (1998) J. Approx. Theory , vol.95 , pp. 388-475
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3
  • 14
    • 0033459230 scopus 로고    scopus 로고
    • Strong asymptotics of orthogonal polynomials with respect to exponential weights
    • [DKMVZ99A]
    • [DKMVZ99A] _, "Strong asymptotics of orthogonal polynomials with respect to exponential weights," Comm. Pure Appl. Math., 52 (1999): 1491-1552.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 1491-1552
  • 15
    • 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
    • [DKMVZ99B]
    • [DKMVZ99B] _, "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): 1335-1425.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 1335-1425
  • 17
    • 84990578228 scopus 로고
    • The collisionless shock region for the long-time behavior of solutions of the KdV equation
    • [DVZ94]
    • [DVZ94] P. Deift, S. Venakides, and X. Zhou, "The collisionless shock region for the long-time behavior of solutions of the KdV equation," Comm. Pure Appl. Math., 47 (1994): 199-206.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 199-206
    • Deift, P.1    Venakides, S.2    Zhou, X.3
  • 18
    • 1842665167 scopus 로고    scopus 로고
    • New results in small dispersion KdV by an extension of the steepest descent method for Riemann-Hilbert problems
    • [DVZ97]
    • [DVZ97] _, "New results in small dispersion KdV by an extension of the steepest descent method for Riemann-Hilbert problems," Internat. Math. Res. Notices, 1997, 285-299.
    • (1997) Internat. Math. Res. Notices , pp. 285-299
  • 19
    • 0001525213 scopus 로고
    • A steepest descent method for oscillatory Riemann-Hilbert problems: Asymptotics for the mKdV equation
    • [DZ93]
    • [DZ93] P. Deift and X. Zhou, "A steepest descent method for oscillatory Riemann-Hilbert problems: asymptotics for the mKdV equation," Ann. of Math. (2), 137 (1993): 295-368.
    • (1993) Ann. of Math. (2) , vol.137 , pp. 295-368
    • Deift, P.1    Zhou, X.2
  • 20
    • 84990647031 scopus 로고
    • Asymptotics for the Painlevé II equation
    • [DZ95]
    • [DZ95] _, "Asymptotics for the Painlevé II equation" Comm. Pure Appl. Math., 48 (1995): 277-337.
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 277-337
  • 21
    • 84928007477 scopus 로고
    • Theta functions and non-linear equations
    • [D81]
    • [D81] B. A. Dubrovin, "Theta functions and non-linear equations," Russian Math. Survey, 36 (1981): 11-92.
    • (1981) Russian Math. Survey , vol.36 , pp. 11-92
    • Dubrovin, B.A.1
  • 24
    • 0002412295 scopus 로고
    • Geometry and modulation theory for the periodic nonlinear Schrödinger equation
    • [FL86], C. Dafermos et al. eds., IMA Volumes in Mathematics and Its Applications, Springer-Verlag, New York
    • [FL86] M. G. Forest and J.-E. Lee, "Geometry and modulation theory for the periodic nonlinear Schrödinger equation" in Oscillation Theory, Computation, and Methods of Compensated Compactness, C. Dafermos et al. eds., IMA Volumes in Mathematics and Its Applications, Vol. 2, Springer-Verlag, New York, 1986, 35-69.
    • (1986) Oscillation Theory, Computation, and Methods of Compensated Compactness , vol.2 , pp. 35-69
    • Forest, M.G.1    Lee, J.-E.2
  • 25
    • 0347468632 scopus 로고    scopus 로고
    • Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers
    • [FM98]
    • [FM98] M. G. Forest and K. T.-R. McLaughlin, "Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers," J. Nonlinear Sci., 8 (1998): 43-62.
    • (1998) J. Nonlinear Sci. , vol.8 , pp. 43-62
    • Forest, M.G.1    McLaughlin, K.T.-R.2
  • 26
    • 0000805694 scopus 로고
    • Equilibrium distributions and the rate of rational approximation of analytic functions
    • [GR87]
    • [GR87] A. A. Gonchar and E. A. Rakhmanov, "Equilibrium distributions and the rate of rational approximation of analytic functions" (in Russian) Math. Sb. (N.S.), 134/176 (1987): 306-352, 447; transl. in Math. USSR-Sb., 62 (1989): 305-348.
    • (1987) Math. Sb. (N.S.) , vol.134-176 , pp. 306-352
    • Gonchar, A.A.1    Rakhmanov, E.A.2
  • 27
    • 33645378339 scopus 로고
    • [GR87]
    • [GR87] A. A. Gonchar and E. A. Rakhmanov, "Equilibrium distributions and the rate of rational approximation of analytic functions" (in Russian) Math. Sb. (N.S.), 134/176 (1987): 306-352, 447; transl. in Math. USSR-Sb., 62 (1989): 305-348.
    • (1989) Math. USSR-Sb. , vol.62 , pp. 305-348
  • 28
    • 0033438093 scopus 로고    scopus 로고
    • The semiclassical limit of the defocusing NLS hierarchy
    • [JLM99]
    • [JLM99] S. Jin, C. D. Levermore, and D. W. McLaughlin, "The semiclassical limit of the defocusing NLS hierarchy," Comm. Pure Appl. Math., 52 (1999): 613-654.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 613-654
    • Jin, S.1    Levermore, C.D.2    McLaughlin, D.W.3
  • 29
    • 0141630526 scopus 로고
    • The collisionless shock phenomenon for the focusing nonlinear Schrödinger equation
    • [K95]
    • [K95] S. Kamvissis, "The collisionless shock phenomenon for the focusing nonlinear Schrödinger equation," C. R. Acad. Sci. Paris Ser. I, 321 (1995): 1525-1531.
    • (1995) C. R. Acad. Sci. Paris Ser. I , vol.321 , pp. 1525-1531
    • Kamvissis, S.1
  • 30
    • 0030514579 scopus 로고    scopus 로고
    • Long time behavior for the focusing nonlinear Schrödinger equation with real spectral singularities
    • [K96]
    • [K96] _, "Long time behavior for the focusing nonlinear Schrödinger equation with real spectral singularities," Comm. Math. Phys., 180 (1996): 325-343.
    • (1996) Comm. Math. Phys. , vol.180 , pp. 325-343
  • 31
    • 41349122386 scopus 로고    scopus 로고
    • Purely imaginary eigenvalues of Zakharov-Shabat systems
    • [KS02]
    • [KS02] M. Klaus and J. K. Shaw, "Purely imaginary eigenvalues of Zakharov-Shabat systems," Phys. Rev. E, 65 (2002): 36607-36611.
    • (2002) Phys. Rev. E , vol.65 , pp. 36607-36611
    • Klaus, M.1    Shaw, J.K.2
  • 32
    • 84990575581 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries equation, I, II, III
    • [LL83]
    • [LL83] P. D. Lax and C. D. Levermore, "The small dispersion limit of the Korteweg-de Vries equation, I, II, III," Comm. Pure Appl. Math., 36 (1983): 253-290, 571-593, 809-830.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 253-290
    • Lax, P.D.1    Levermore, C.D.2
  • 33
    • 0035873340 scopus 로고    scopus 로고
    • Some remarks on a WKB method for the nonselfadjoint Zakharov-Shabat eigenvalue problem with analytic potentials and fast phase
    • [M01]
    • [M01] P. D. Miller, "Some remarks on a WKB method for the nonselfadjoint Zakharov-Shabat eigenvalue problem with analytic potentials and fast phase," Phys. D, 152-153 (2001): 145-162.
    • (2001) Phys. D , vol.152-153 , pp. 145-162
    • Miller, P.D.1
  • 34
    • 0036335780 scopus 로고    scopus 로고
    • Asymptotics of semiclassical soliton ensembles: Rigorous justification of the WKB approximation
    • [M02]
    • [M02] _, "Asymptotics of semiclassical soliton ensembles: rigorous justification of the WKB approximation," Internat. Math. Res. Notices, 2002, 383-54.
    • (2002) Internat. Math. Res. Notices , pp. 383-454
  • 35
    • 0002023137 scopus 로고    scopus 로고
    • On the semiclassical limit of the focusing nonlinear Schrödinger equation
    • [MK98]
    • [MK98] P. D. Miller and S. Kamvissis, "On the semiclassical limit of the focusing nonlinear Schrödinger equation," Phys. Lett. A, 247 (1998): 75-86.
    • (1998) Phys. Lett. A , vol.247 , pp. 75-86
    • Miller, P.D.1    Kamvissis, S.2
  • 36
    • 0004026391 scopus 로고
    • [M53], Dover, New York. Second edition published by P. Noordhoff N. V., Groningen, Holland
    • [M53] N. I. Muskhelishvili, Singular Integral Equations, Dover, New York, 1992. Second edition published by P. Noordhoff N. V., Groningen, Holland, 1953.
    • (1953) Singular Integral Equations
    • Muskhelishvili, N.I.1
  • 41
    • 0001000124 scopus 로고
    • Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media
    • [SY74]
    • [SY74] J. Satsuma and N. Yajima, "Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media," Supp. Prog. Theo. Phys., 55 (1974): 284-306.
    • (1974) Supp. Prog. Theo. Phys. , vol.55 , pp. 284-306
    • Satsuma, J.1    Yajima, N.2
  • 43
    • 0141854055 scopus 로고
    • Some recent developments in the theory of conformal mapping
    • [S50], appendix to R. Courant, Interscience, New York
    • [S50] M. Schiffer, "Some recent developments in the theory of conformal mapping," appendix to R. Courant, Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces, Interscience, New York, 1950.
    • (1950) Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces
    • Schiffer, M.1
  • 44
    • 0039741902 scopus 로고    scopus 로고
    • The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases
    • [TV00]
    • [TV00] A. Tovbis and S. Venakides, "The eigenvalue problem for the focusing nonlinear Schrödinger equation: new solvable cases," Phys. D, 146 (2000): 150-164.
    • (2000) Phys. D , vol.146 , pp. 150-164
    • Tovbis, A.1    Venakides, S.2
  • 46
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • [ZS72]
    • [ZS72] V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP, 34 (1972): 62-69.
    • (1972) Sov. Phys. JETP , vol.34 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2
  • 47
    • 0000509583 scopus 로고
    • The Riemann-Hilbert problem and inverse scattering
    • [Z89]
    • [Z89] X. Zhou, "The Riemann-Hilbert problem and inverse scattering," SIAM J. Math. Anal., 20 (1989): 966-986.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 966-986
    • Zhou, X.1


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