Dept. Math, Hokkaido Univ. EPrints Server

Nonlinear Schr\"odinger equation with a point defect

Preprint Series # 768
Fukuizumi, Reika and Ohta, Masahito and Ozawa, Tohru Nonlinear Schr\"odinger equation with a point defect. (2006);

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Abstract

We study nonlinear Schr\"odinger equation with a delta-function impurity in one space dimension. Global well-posedness is proved for the Cauchy problem in $L^2(\R)$ under subcritical nonlinearity, as well as under critical nonlinearity with smallness assumption on the data. In the attractive case, orbital stability and instability of the ground state is proved in $H^1(\R)$.

Item Type:Preprint
Uncontrolled Keywords:nonlinear Schr\"odinger equation with a delta potential, global well-posedness of the Cauchy problem, orbital stability and instability of the ground state
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1261