Asymptotics of oscillatory Riemann–Hilbert problems

DOI10.1063/1.531706zbMath0860.35091OpenAlexW1963600437MaRDI QIDQ4716496

G. G. Varzugin

Publication date: 26 November 1996

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531706

zbMATH Keywords

oscillatory Riemann-Hilbert problemslong-time behavior of the solutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (9)

Long-time asymptotics for the Korteweg-de Vries equation via nonlinear steepest descent ⋮ Quasiclassical asymptotics for solutions of the matrix conjugation problem with rapid oscillation of off-diagonal entries ⋮ Long-time asymptotics of a three-component coupled nonlinear Schrödinger system ⋮ Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces ⋮ On the Cauchy problem of defocusing mKdV equation with finite density initial data: long time asymptotics in soliton-less regions ⋮ Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data ⋮ An operator van der Corput estimate arising from oscillatory Riemann-Hilbert problems ⋮ A \(\bar{\partial}\)-steepest descent method for oscillatory Riemann-Hilbert problems ⋮ Long time asymptotics for the nonlocal mKdV equation with finite density initial data

Cites Work

• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Scattering and inverse scattering for first order systems
• Caustics in 1+1 integrable systems
• The Riemann–Hilbert Problem and Inverse Scattering

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