|
A steepest descent method for oscillatory Riemann-Hilbert problems
Author(s):
P.
Deift;
X.
Zhou
Journal:
Bull. Amer. Math. Soc.
26
(1992),
119-124.
MSC (1980):
Primary 35Q20;
Secondary 35B40
MathSciNet review:
1108902
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [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. \textbf{14} (1973), 1277--1284. MR 324237
- [AS]
- M. J. Ablowitz and H. Segur, Asymptotic solutions of the Korteweg de Vries equation, Stud. Appl. Math. \textbf{57} (1977), 13--14. MR 481656
- [BC]
- R. Beals and R. Coifman, Scattering and inverse scattering for first order systems, Comm. Pure Appl. Math. \textbf{37} (1984), 39--90. MR 728266
- [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 \textbf{34} (1981), 217--218. MR
- [BS1]
- V. S. Buslaev and V. V. Sukhanov, Asymptotic behavior of solutions of the Korteweg de Vries equation, Proc. Sci. Seminar LOMI {\bf 120} (1982), 32--50. (Russian); transl. in J. Soviet Math. \textbf{34} (1986), 1905--1920. MR 701550
- [BS2]
- V. S. Buslaev and V. V. Sukhanov, On the asymptotic behavior as $t\rightarrow \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. {\bf 10} (1982), 70--102. (Russian); transl. in Selecta Math. Soviet {\bf 4} (1985), 225--248; II, Proc. Sci. Seminar LOMI {\bf 138} (1984), 8--32. (Russian); transl. in J. Soviet Math. {\bf 32} (1986), 426--446; III, Prob. Math. Phys. (M. Birman, ed.) \textbf{11} (1986), 78--113. (Russian). MR 755906
- [I]
- A. R. Its, Asymptotics of solutions of the nonlinear Schr\"odinger equation and isomonodromic deformations of systems of linear differential equations, Soviet Math. Dokl. \textbf{24} (1981), 452--456. MR
- [IN]
- A. R. Its and V. Yu. Novokshenov, The isomonodromic deformation method in the theory of Painlev\'e equations, Lecture Notes in Math., vol. 1191, Springer-Verlag, Berlin and Heidelberg, 1986. MR 851569
- [M]
- S. V. Manakov, Nonlinear Fraunhofer diffraction, Zh. \`Eksper. Teoret. Fiz. {\bf 65} (1973), 1392--1398. (Russian); transl. in Soviet Phys.-JETP, \textbf{38} (1974), 693--696. MR 389107
- [N]
- V. Yu. Novokshenov, Asymptotics as $t\rightarrow \infty $ of the solution of the Cauchy problem for the nonlinear Schr\"odinger equation, Soviet Math. Dokl. \textbf{21} (1980), 529--533. MR
- [ZM]
- V. E. Zakharov and S. V. Manakov, Asymptotic behavior of nonlinear wave systems integrated by the inverse method, Zh. \`Eksper. Teoret. Fiz. {\bf 71} (1976), 203--215. (Russian); transl. in Sov. Phys.-JETP \textbf{44 {\rm (1976), 106--112}}. MR 673411
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1980):
35Q20, 35B40
Retrieve articles in all Journals with MSC
(1980):
35Q20, 35B40
Additional Information:
DOI:
10.1090/S0273-0979-1992-00253-7
PII:
S 0273-0979(1992)00253-7
|
