Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times

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Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times. / Buslaev, V. S.; Sukhanov, V. V.

In: Journal of Soviet Mathematics, Vol. 34, No. 5, 01.09.1986, p. 1905-1920.

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

BibTeX

@article{702d831346d9490ab4cfaa18727c85aa,

title = "Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times",

abstract = "For the KdV equation a complete asymptotic expansion of the {"}dispersive tail{"} for large times is described, and generalized wave operators are introduced. The asymptotics for large times of the spectral Schr{\"o}dinger equation with a potential of the type of a solution of the KdV equation is studied. It is shown that the KdV equation is connected in a specific manner with the structure of the asymptotics of solutions of the spectral equation. As a corollary, known explicit formulas for the leading terms of the asymptotics of solutions of the KdV equation in terms of spectral data corresponding to the initial conditions are obtained. A plan for justifying the results listed is outlined. {\textcopyright} 1986 Plenum Publishing Corporation.",

author = "Buslaev, {V. S.} and Sukhanov, {V. V.}",

year = "1986",

month = sep,

day = "1",

doi = "10.1007/BF01095099",

language = "English",

volume = "34",

pages = "1905--1920",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times

AU - Buslaev, V. S.

AU - Sukhanov, V. V.

PY - 1986/9/1

Y1 - 1986/9/1

N2 - For the KdV equation a complete asymptotic expansion of the "dispersive tail" for large times is described, and generalized wave operators are introduced. The asymptotics for large times of the spectral Schrödinger equation with a potential of the type of a solution of the KdV equation is studied. It is shown that the KdV equation is connected in a specific manner with the structure of the asymptotics of solutions of the spectral equation. As a corollary, known explicit formulas for the leading terms of the asymptotics of solutions of the KdV equation in terms of spectral data corresponding to the initial conditions are obtained. A plan for justifying the results listed is outlined. © 1986 Plenum Publishing Corporation.

AB - For the KdV equation a complete asymptotic expansion of the "dispersive tail" for large times is described, and generalized wave operators are introduced. The asymptotics for large times of the spectral Schrödinger equation with a potential of the type of a solution of the KdV equation is studied. It is shown that the KdV equation is connected in a specific manner with the structure of the asymptotics of solutions of the spectral equation. As a corollary, known explicit formulas for the leading terms of the asymptotics of solutions of the KdV equation in terms of spectral data corresponding to the initial conditions are obtained. A plan for justifying the results listed is outlined. © 1986 Plenum Publishing Corporation.

UR - http://www.scopus.com/inward/record.url?scp=0002289261&partnerID=8YFLogxK

U2 - 10.1007/BF01095099

DO - 10.1007/BF01095099

M3 - Article

AN - SCOPUS:0002289261

VL - 34

SP - 1905

EP - 1920

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 127654995