Differential and Integral Equations

Nonexistence of scattering states for some quadratic nonlinear Schrödinger equations in two space dimensions

Akihiro Shimomura and Yoshio Tsutsumi

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Abstract

In this paper, we study the large-time behavior of solutions to the Schrödinger equation with the quadratic nonlinearity $\lambda |u|^2$ with $\lambda \in \mathbb{C} \setminus \{ 0 \}$ in two space dimensions. The nonexistence of non-trivial scattering states for this equation is proved without assuming a convergence rate for the difference between a solution to the nonlinear equation and a free solution.

Article information

Source
Differential Integral Equations, Volume 19, Number 9 (2006), 1047-1060.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050332

Mathematical Reviews number (MathSciNet)
MR2262096

Zentralblatt MATH identifier
1212.35021

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; Tsutsumi, Yoshio. Nonexistence of scattering states for some quadratic nonlinear Schrödinger equations in two space dimensions. Differential Integral Equations 19 (2006), no. 9, 1047--1060. https://projecteuclid.org/euclid.die/1356050332


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