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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

A steepest descent method for oscillatory Riemann-Hilbert problems

Author(s): P. Deift; X. Zhou
Journal: Bull. Amer. Math. Soc. 26 (1992), 119-123.
MSC (2000): Primary 35Q15; Secondary 35B40, 35Q53, 41A60
MathSciNet review: 1108902
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References | Similar articles | Additional information

References:

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M. J. Ablowitz and H. Segur, Asymptotic solutions of the Korteweg de Vries equation, Stud. Appl. Math. 57 (1977), 13-14. MR 0481656 (58:1757)

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R. Beals and R. Coifman, Scattering and inverse scattering for first order systems, Comm. Pure Appl. Math. 37 (1984), 39-90. MR 728266 (85f:34020)

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V. S. Buslaev, Use of the determinant representation of solutions of the Korteweg de Vries equation for the investigation of their asymptotic behavior for large times, Uspekhi Mat. Nauk 34 (1981), 217-218.

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V. S. Buslaev and V. V. Sukhanov, Asymptotic behavior of solutions of the Korteweg de Vries equation, Proc. Sci. Seminar LOMI 120 (1982), 32-50. (Russian); transl. in J. Soviet Math. 34 (1986), 1905-1920. MR 701550 (85f:35169)

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-, On the asymptotic behavior as $ t \to \infty $ of the solutions of the equation $ {\psi _{xx}} + u(x,t)\psi + (\lambda /4)\psi = 0$ with potential u satisfying the Korteweg de Vries equation, I, Prob. Math. Phys. 10 (1982), 70-102. (Russian); transl. in Selecta Math. Soviet 4, (1985), 225-248; II, Proc. Sci. Seminar LOMI 138 (1984), 8-32. (Russian); transl. in J. Soviet Math. 32 (1986), 426-446; III, Prob. Math. Phys. (M. Birman, ed.) 11 (1986), 78-113. (Russian) MR 755906 (86a:35122)

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A. R. Its, Asymptotics of solutions of the nonlinear Schrödinger equation and isomonodromic deformations of systems of linear differential equations, Soviet Math. Dokl. 24 (1981), 452-456.

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A. R. Its and V. Yu. Novokshenov, The isomonodromic deformation method in the theory of Painlevé equations, Lecture Notes in Math., vol. 1191, Springer-Verlag, Berlin and Heidelberg, 1986. MR 851569 (89b:34012)

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S. V. Manakov, Nonlinear Fraunhofer diffraction, Zh. Èksper. Teoret. Fiz. 65 (1973), 1392-1398. (Russian); transl. in Soviet Phys.-JETP, 38 (1974), 693-696.

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V. Yu. Novokshenov, Asymptotics as $ t \to \infty $ of the solution of the Cauchy problem for the nonlinear Schrödinger equation, Soviet Math. Dokl. 21 (1980), 529-533.

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Additional Information:

DOI: 10.1090/S0273-0979-1992-00253-7
PII: S 0273-0979(1992)00253-7
Copyright of article: Copyright 1992, American Mathematical Society




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