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International Mathematics Research Notices (2000) 2000:115-132, doi:10.1155/S1073792800000088
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

On the quadratic nonlinear Schrödinger equation in three space dimensions

Nakao Hayashi and Pavel I. Naumkin

We study the global in time existence of small solutions to the quadratic nonlinear Schrodinger equation

Formula
, where the nonlinear term Formula.

We prove the global existence of solutions to the Cauchy problem (A) under the condition that the initial data Formula are sufficiently small, where Formula is the weighted Sobolev space. We also show the existence of the usual scattering states.


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Global Solutions for 3D Quadratic Schrodinger Equations
Int Math Res Notices, January 1, 2009; 2009(3): 414 - 432.
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