A steepest descent method for oscillatory Riemann-Hilbert problems

Authors:
P. Deift and X. Zhou

Journal:
Bull. Amer. Math. Soc. **26** (1992), 119-123

MSC (2000):
Primary 35Q15; Secondary 35B40, 35Q53, 41A60

DOI:
https://doi.org/10.1090/S0273-0979-1992-00253-7

MathSciNet review:
1108902

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References | Similar Articles | Additional Information

**[AN]**Mark J. Ablowitz and Alan C. Newell,*The decay of the continuous spectrum for solutions of the Korteweg-de Vries equation*, J. Mathematical Phys.**14**(1973), 1277–1284. MR**0324237**, https://doi.org/10.1063/1.1666479**[AS]**M. J. Ablowitz and H. Segur,*Asymptotic solutions of the Korteweg-deVries equation*, Studies in Appl. Math.**57**(1976/77), no. 1, 13–44. MR**0481656****[BC]**R. Beals and R. R. Coifman,*Scattering and inverse scattering for first order systems*, Comm. Pure Appl. Math.**37**(1984), no. 1, 39–90. MR**728266**, https://doi.org/10.1002/cpa.3160370105**[B]**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.**[BS1]**V. S. Buslaev and V. V. Sukhanov,*Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times*, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)**120**(1982), 32–50 (Russian, with English summary). Questions in quantum field theory and statistical physics, 3. MR**701550****[BS2]**V. S. Buslaev and V. V. Sukhanov,*Asymptotic behavior as 𝑡→∞ of the solutions of the equation 𝜓ₓₓ+𝑢(𝑥,𝑡)𝜓+(𝜆/4)𝜓=0 with a potential 𝑢 satisfying the Korteweg-de Vries equation. II*, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)**138**(1984), 8–32 (Russian, with English summary). Boundary value problems of mathematical physics and related problems in the theory of functions, 16. MR**755906****[I]**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.**[IN]**Alexander R. Its and Victor Yu. Novokshenov,*The isomonodromic deformation method in the theory of Painlevé equations*, Lecture Notes in Mathematics, vol. 1191, Springer-Verlag, Berlin, 1986. MR**851569****[M]**S. V. Manakov,*Nonlinear Fraunhofer diffraction*, Zh. Èksper. Teoret. Fiz.**65**(1973), 1392-1398. (Russian); transl. in Soviet Phys.-JETP,**38**(1974), 693-696.**[N]**V. Yu. Novokshenov,*Asymptotics as of the solution of the Cauchy problem for the nonlinear Schrödinger equation*, Soviet Math. Dokl.**21**(1980), 529-533.**[ZM]**V. E. Zakharov and S. V. Manakov,*Asymptotic behavior of non-linear wave systems integrated by the inverse scattering method*, Z. Èksper. Teoret. Fiz.**71**(1976), no. 1, 203–215 (Russian, with English summary); English transl., Soviet Physics JETP**44**(1976), no. 1, 106–112. MR**0673411**

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DOI:
https://doi.org/10.1090/S0273-0979-1992-00253-7

Article copyright:
© Copyright 1992
American Mathematical Society