论文信息 - A steepest descent method for oscillatory Riemann-Hilbert problems

A steepest descent method for oscillatory Riemann-Hilbert problems

In this article we present a new and general approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, when evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves here exclusively to the modified Korteweg-de Vries (MKdV) equation

P. Deift | Xin Zhou

[1] Xin Zhou. The Riemann-Hilbert problem and inverse scattering , 1989 .

[2] V. Sukhanov,et al. Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times , 1986 .

[3] V. Buslaev. Asymptotic behavior of solutions of the Korteweg-de Vries equation , 1986 .

[4] Alexander Its,et al. Isomonodromic Deformation Method in the Theory of Painleve Equations , 1986 .

[5] Ronald R. Coifman,et al. Scattering and inverse scattering for first order systems , 1984 .

[6] V. Sukhanov. Asymptotic behavior of solutions of the Cauchy problem for a system of the KdV type for large times , 1983 .

[7] Michio Jimbo,et al. Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III , 1981 .

[8] A. Newell,et al. Monodromy- and spectrum-preserving deformations I , 1980 .

[9] M. Ablowitz,et al. Asymptotic Solutions of the Korteweg-deVries Equation , 1977 .

[10] S. V. Manakov,et al. Nonlinear Fraunhofer diffraction , 1974 .

[11] M. Ablowitz,et al. The decay of the continuous spectrum for solutions of the Korteweg‐deVries equation , 1973 .

[12] V. Karpman. An asymptotic solution of the Korteweg-De Vries equation , 1967 .

[13] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[14] W. Wasow. Asymptotic expansions for ordinary differential equations , 1965 .

[15] Edmund Taylor Whittaker,et al. A Course of Modern Analysis , 2021 .