## Differential and Integral Equations

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

#### 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