Large time asymptotics for the cylindrical Korteweg-de Vries equation. I.

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Large time asymptotics for the cylindrical Korteweg-de Vries equation. I. / Its, A.; Sukhanov, V.

In: Nonlinearity, Vol. 33, No. 10, 10.2020, p. 5215-5245.

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

BibTeX

@article{c8b9549b7c544c83bff82abd7ae45344,

title = "Large time asymptotics for the cylindrical Korteweg-de Vries equation. I.",

abstract = "This paper is the first part of our study the asymptotic behavior of the solutions of the cylindrical Korteweg-de Vries equation (cKdV). In this first part, we consider the solutions from Schwarz's class and calculate the large time asymptotics using the method based on the asymptotic solution of the associated direct scattering problem. This approach was first suggested, in the cases of usual KdV and NLS equations, in the late 70s by Zakharov and Manakov. In a sequel to this paper, we plan to calculate the large time asymptotics of some other classes of solutions of the cKdV equation which exhibit the oscillatory type behavior, and we will also evaluate the short time asymptotics of the solutions of the cKdV equation. In the second part we will use the Defit-Zhou nonlinear steepest descent method for oscillatory Riemann-Hilbert problems. ",

keywords = "Cauchy problem, Cylindrical korteweg-de vries equation, Large time asymptotics",

author = "A. Its and V. Sukhanov",

note = "Publisher Copyright: {\textcopyright} 2020 IOP Publishing Ltd & London Mathematical Society.",

year = "2020",

month = oct,

doi = "10.1088/1361-6544/ab9496",

language = "English",

volume = "33",

pages = "5215--5245",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "10",

}

RIS

TY - JOUR

T1 - Large time asymptotics for the cylindrical Korteweg-de Vries equation. I.

AU - Its, A.

AU - Sukhanov, V.

PY - 2020/10

Y1 - 2020/10

N2 - This paper is the first part of our study the asymptotic behavior of the solutions of the cylindrical Korteweg-de Vries equation (cKdV). In this first part, we consider the solutions from Schwarz's class and calculate the large time asymptotics using the method based on the asymptotic solution of the associated direct scattering problem. This approach was first suggested, in the cases of usual KdV and NLS equations, in the late 70s by Zakharov and Manakov. In a sequel to this paper, we plan to calculate the large time asymptotics of some other classes of solutions of the cKdV equation which exhibit the oscillatory type behavior, and we will also evaluate the short time asymptotics of the solutions of the cKdV equation. In the second part we will use the Defit-Zhou nonlinear steepest descent method for oscillatory Riemann-Hilbert problems.

AB - This paper is the first part of our study the asymptotic behavior of the solutions of the cylindrical Korteweg-de Vries equation (cKdV). In this first part, we consider the solutions from Schwarz's class and calculate the large time asymptotics using the method based on the asymptotic solution of the associated direct scattering problem. This approach was first suggested, in the cases of usual KdV and NLS equations, in the late 70s by Zakharov and Manakov. In a sequel to this paper, we plan to calculate the large time asymptotics of some other classes of solutions of the cKdV equation which exhibit the oscillatory type behavior, and we will also evaluate the short time asymptotics of the solutions of the cKdV equation. In the second part we will use the Defit-Zhou nonlinear steepest descent method for oscillatory Riemann-Hilbert problems.

KW - Cauchy problem

KW - Cylindrical korteweg-de vries equation

KW - Large time asymptotics

UR - http://www.scopus.com/inward/record.url?scp=85092333551&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/ab9496

DO - 10.1088/1361-6544/ab9496

M3 - Article

AN - SCOPUS:85092333551

VL - 33

SP - 5215

EP - 5245

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 10

ER -

ID: 87673679