Differential and Integral Equations

Nonexistence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in two space dimensions

Akihiro Shimomura

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Abstract

In this paper, the asymptotic behavior in time of solutions for the nonlinear Schrödinger equation with the quadratic nonlinearity $\lambda |u|^2$ with $\lambda \in {\mathbb C} \setminus \{ 0 \}$ in two space dimensions is studied. The nonexistence of asymptotically free solutions for this equation is proved.

Article information

Source
Differential Integral Equations, Volume 18, Number 3 (2005), 325-335.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060222

Mathematical Reviews number (MathSciNet)
MR2122723

Zentralblatt MATH identifier
1212.35020

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions 35P25: Scattering theory [See also 47A40]

Citation

Shimomura, Akihiro. Nonexistence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in two space dimensions. Differential Integral Equations 18 (2005), no. 3, 325--335. https://projecteuclid.org/euclid.die/1356060222


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