## Differential and Integral Equations

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

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

#### 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