Differential and Integral Equations

The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line

Justin Holmer

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Abstract

We prove, by adapting the method of Colliander-Kenig [9], local well posedness of the initial-boundary-value problem for the one-dimensional nonlinear Schrödinger equation $i\partial_tu +\partial_x^2u +\lambda u|u|^{\alpha-1}=0$ on the half-line under low boundary regularity assumptions.

Article information

Source
Differential Integral Equations, Volume 18, Number 6 (2005), 647-668.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060174

Mathematical Reviews number (MathSciNet)
MR2136703

Zentralblatt MATH identifier
1212.35448

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Holmer, Justin. The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line. Differential Integral Equations 18 (2005), no. 6, 647--668. https://projecteuclid.org/euclid.die/1356060174


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