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

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[AN]**M. J. Ablowitz and A. C. Newell,*The decay of the continuous spectrum for solutions of the Korteweg de Vries equation*, J. Math. Phys.**14**(1973), 1277-1284. MR**0324237 (48:2589)****[AS]**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)****[BC]**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)****[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*, Proc. Sci. Seminar LOMI**120**(1982), 32-50. (Russian); transl. in J. Soviet Math.**34**(1986), 1905-1920. MR**701550 (85f:35169)****[BS2]**-,*On the asymptotic behavior as of the solutions of the equation 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)****[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]**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)****[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 nonlinear wave systems integrated by the inverse method*, Zh. Èksper. Teoret. Fiz.**71**(1976), 203-215. (Russian); transl. in Sov. Phys.-JETP**44**(1976), 106-112. MR**0673411 (58:32546)**

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Additional Information

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

Article copyright:
© Copyright 1992
American Mathematical Society