Singular matrix conjugacy problem with rapidly oscillating off-diagonal entries. Asymptotics of the solution in the case when a diagonal entry vanishes at a stationary point

DOI10.1090/SPMJ/1673zbMath1483.35144OpenAlexW3197368714MaRDI QIDQ5155637

A. M. Budylin

Publication date: 8 October 2021

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/spmj/1673

zbMATH Keywords

singular integral equationsnonlinear equationsquasiclassical asymptoticsmatrix conjugacy problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Riemann-Hilbert problems in context of PDEs (35Q15) Singular integral equations (45E99)

Cites Work

• Quasi-classical asymptotics of solutions to the matrix factorization problem with quadratically oscillating off-diagonal elements
• A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• The collisionless shock region for the long‐time behavior of solutions of the KdV equation
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