Dept. Math, Hokkaido Univ. EPrints Server

SMOOTHING EFFECT AND LARGE TIME BEHAVIOR OF SOLUTIONS TO SCHR\"ODINGER EQUATIONS WITH NONLINEARITY OF INTEGRAL TYPE

Preprint Series # 600
Ozawa, Tohru and Yamazaki, Yasuko SMOOTHING EFFECT AND LARGE TIME BEHAVIOR OF SOLUTIONS TO SCHR\"ODINGER EQUATIONS WITH NONLINEARITY OF INTEGRAL TYPE. (2003);

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Abstract

We study the smoothing effect in space and asymptotic behavior in time of solutions to the Cauchy problem for the nonlinear Schr\"odinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. A detailed description is given on the phase modification of scattering solutions by taking into account the long range effect of the interaction.

Item Type:Preprint
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:70