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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. (English. Russian original) Zbl 1483.35144

St. Petersbg. Math. J. 32, No. 5, 847-864 (2021); translation from Algebra Anal. 32, No. 5, 37-61 (2020).
In this paper, the author considers a \(2 \times 2\) matrix conjugation problem (the Riemann-Hilbert factorization problem) with rapidly oscillating off-diagonal inputs and a quadratic phase function, in particular when one of the diagonal inputs vanishes at a stationary point. The main result here is the determination of the leading term with respect to time asymptotics of the solution of this problem.

MSC:

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