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