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Nonlinear Schrödinger equation with a point defect

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 Title: Nonlinear Schrödinger equation with a point defect Authors: Fukuizumi, Reika Browse this author Ohta, Masahito Browse this author Ozawa, Tohru Browse this author Keywords: nonlinear Schr\"odinger equation with a delta potential global well-posedness of the Cauchy problem orbital stability and instability of the ground state Issue Date: 2006 Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 768 Start Page: 1 End Page: 14 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 $H^1(\R)$. Type: bulletin (article) URI: http://hdl.handle.net/2115/69576 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics