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Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line. / de Monvel, Anne Boutet; Its, Alexander; Kotlyarov, Vladimir.

в: Communications in Mathematical Physics, Том 290, № 2, 07.2009, стр. 479-522.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

de Monvel, AB, Its, A & Kotlyarov, V 2009, 'Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line', Communications in Mathematical Physics, Том. 290, № 2, стр. 479-522. https://doi.org/10.1007/s00220-009-0848-7

APA

de Monvel, A. B., Its, A., & Kotlyarov, V. (2009). Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line. Communications in Mathematical Physics, 290(2), 479-522. https://doi.org/10.1007/s00220-009-0848-7

Vancouver

de Monvel AB, Its A, Kotlyarov V. Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line. Communications in Mathematical Physics. 2009 Июль;290(2):479-522. https://doi.org/10.1007/s00220-009-0848-7

Author

de Monvel, Anne Boutet ; Its, Alexander ; Kotlyarov, Vladimir. / Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line. в: Communications in Mathematical Physics. 2009 ; Том 290, № 2. стр. 479-522.

BibTeX

@article{6cafd21040844886aa21ee2ef2c6db67,
title = "Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line",
abstract = "We consider the focusing nonlinear Schr{\"o}dinger equation on the quarter plane. The initial data are vanishing at infinity while the boundary data are time- periodic, of the form. The goal of this paper is to study the asymptotic behavior of the solution of this initial-boundary-value problem. The main tool is the asymptotic analysis of an associated matrix Riemann-Hilbert problem. We show that for the solution of the IBV problem has different asymptotic behaviors in different regions. In the region, where, the solution takes the form of the Zakharov-Manakov vanishing asymptotics. In a region of type, where N is any integer, the solution is asymptotic to a train of asymptotic solitons. In the region, the solution takes the form of a modulated elliptic wave. In the region, the solution takes the form of a plane wave.",
author = "{de Monvel}, {Anne Boutet} and Alexander Its and Vladimir Kotlyarov",
year = "2009",
month = jul,
doi = "10.1007/s00220-009-0848-7",
language = "English",
volume = "290",
pages = "479--522",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line

AU - de Monvel, Anne Boutet

AU - Its, Alexander

AU - Kotlyarov, Vladimir

PY - 2009/7

Y1 - 2009/7

N2 - We consider the focusing nonlinear Schrödinger equation on the quarter plane. The initial data are vanishing at infinity while the boundary data are time- periodic, of the form. The goal of this paper is to study the asymptotic behavior of the solution of this initial-boundary-value problem. The main tool is the asymptotic analysis of an associated matrix Riemann-Hilbert problem. We show that for the solution of the IBV problem has different asymptotic behaviors in different regions. In the region, where, the solution takes the form of the Zakharov-Manakov vanishing asymptotics. In a region of type, where N is any integer, the solution is asymptotic to a train of asymptotic solitons. In the region, the solution takes the form of a modulated elliptic wave. In the region, the solution takes the form of a plane wave.

AB - We consider the focusing nonlinear Schrödinger equation on the quarter plane. The initial data are vanishing at infinity while the boundary data are time- periodic, of the form. The goal of this paper is to study the asymptotic behavior of the solution of this initial-boundary-value problem. The main tool is the asymptotic analysis of an associated matrix Riemann-Hilbert problem. We show that for the solution of the IBV problem has different asymptotic behaviors in different regions. In the region, where, the solution takes the form of the Zakharov-Manakov vanishing asymptotics. In a region of type, where N is any integer, the solution is asymptotic to a train of asymptotic solitons. In the region, the solution takes the form of a modulated elliptic wave. In the region, the solution takes the form of a plane wave.

UR - http://www.scopus.com/inward/record.url?scp=70350626804&partnerID=8YFLogxK

U2 - 10.1007/s00220-009-0848-7

DO - 10.1007/s00220-009-0848-7

M3 - Article

AN - SCOPUS:70350626804

VL - 290

SP - 479

EP - 522

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -

ID: 97808139