SCATTERING FOR A NONLINEAR SCHRODINGER EQUATION WITH A POTENTIAL

초록

We consider a 3d cubic focusing nonlinear Schrodinger equation with a potential I partial derivative(t)u + Delta u - Vu + vertical bar u vertical bar(2)u = 0 where V is a real-valued short-range potential having a small negative part. We find criteria for global well-posedness analogous to the homogeneous case V = 0 [10, 5]. Moreover, by the concentration-compactness approach, we prove that if V is repulsive, such global solutions scatter.

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