## Differential and Integral Equations

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

Akihiro Shimomura

#### 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