Nonlinear Steepest Descent and Numerical Solution of Riemann‐Hilbert Problems

DOI10.1002/cpa.21497zbMath1300.65094arXiv1205.5604OpenAlexW2964249937MaRDI QIDQ5495874

Thomas Trogdon, Sheehan Olver

Publication date: 7 August 2014

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.5604

zbMATH Keywords

singular integral equationsPainlevé II equationRiemann-Hilbert problemsKorteweg de Vries equationmethod of nonlinear steepest descent

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Integral equations with kernels of Cauchy type (45E05)

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Cites Work

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• A Riemann-Hilbert problem for the finite-genus solutions of the KdV equation and its numerical solution
• Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations
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• Numerical solution of Riemann-Hilbert problems: Painlevé II
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Higher-order analogues of the Tracy-Widom distribution and the Painlevé II hierarchy
• A steepest descent method for oscillatory Riemann-Hilbert problems
• The Riemann–Hilbert Problem and Inverse Scattering

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