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

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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. / Будылин, Александр Михайлович.

In: St. Petersburg Mathematical Journal, Vol. 32, No. 5, 10.2021, p. 847-864 .

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{560c9253381c4c20a60b267a5ead1e6a,

title = "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",

abstract = "The (2 × 2) matrix conjugacy problem (the Riemann—Hilbert problem) with rapidly oscillating off-diagonal entries and quadratic phase function is considered, specifically, the case when one of the diagonal entries vanishes at a stationary point. For solutions of this problem, the leading term of the asymptotics is found. However, the method allows us to construct complete expansions in power orders. These asymptotics can be used, for example, to construct the asymptotics of solutions of the Cauchy problem for the nonlinear Schr{\"o}dinger equation for large times in the case of the so-called collisionless shock region.",

keywords = "Matrix conjugacy problem, nonlinear equations of mathematical physics, quasiclassical asymptotics, singular integral equations, singular integral equa-tions",

author = "Будылин, {Александр Михайлович}",

note = "Publisher Copyright: {\textcopyright} 2021. American Mathematical Society.",

year = "2021",

month = oct,

doi = "10.1090/spmj/1673",

language = "English",

volume = "32",

pages = "847--864 ",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "5",

}

RIS

TY - JOUR

T1 - 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

AU - Будылин, Александр Михайлович

PY - 2021/10

Y1 - 2021/10

N2 - The (2 × 2) matrix conjugacy problem (the Riemann—Hilbert problem) with rapidly oscillating off-diagonal entries and quadratic phase function is considered, specifically, the case when one of the diagonal entries vanishes at a stationary point. For solutions of this problem, the leading term of the asymptotics is found. However, the method allows us to construct complete expansions in power orders. These asymptotics can be used, for example, to construct the asymptotics of solutions of the Cauchy problem for the nonlinear Schrödinger equation for large times in the case of the so-called collisionless shock region.

AB - The (2 × 2) matrix conjugacy problem (the Riemann—Hilbert problem) with rapidly oscillating off-diagonal entries and quadratic phase function is considered, specifically, the case when one of the diagonal entries vanishes at a stationary point. For solutions of this problem, the leading term of the asymptotics is found. However, the method allows us to construct complete expansions in power orders. These asymptotics can be used, for example, to construct the asymptotics of solutions of the Cauchy problem for the nonlinear Schrödinger equation for large times in the case of the so-called collisionless shock region.

KW - Matrix conjugacy problem

KW - nonlinear equations of mathematical physics

KW - quasiclassical asymptotics

KW - singular integral equations

KW - singular integral equa-tions

UR - http://www.scopus.com/inward/record.url?scp=85114248256&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/367624d2-2995-32dc-827e-82cb6701d077/

U2 - 10.1090/spmj/1673

DO - 10.1090/spmj/1673

M3 - Article

VL - 32

SP - 847

EP - 864

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -

ID: 85305641