Nonlinear Schrödinger Equations and Their Spectral Semi-Discretizations Over Long Times

Nonlinear Schrödinger Equations and Their Spectral Semi-Discretizations Over Long Times: "

Abstract Cubic Schrödinger equations with small initial data (or small nonlinearity) and their spectral semi-discretizations in space
are analyzed. It is shown that along both the solution of the nonlinear Schrödinger equation as well as the solution of the
semi-discretized equation the actions of the linear Schrödinger equation are approximately conserved over long times. This
also allows us to show approximate conservation of energy and momentum along the solution of the semi-discretized equation
over long times. These results are obtained by analyzing a modulated Fourier expansion in time. They are valid in arbitrary
spatial dimension.

• Content Type Journal Article
• DOI 10.1007/s10208-010-9059-z
• Authors
  
  
  • Ludwig Gauckler, Universität Tübingen Mathematisches Institut Auf der Morgenstelle 10 D-72076 Tübingen Germany
  • Christian Lubich, Universität Tübingen Mathematisches Institut Auf der Morgenstelle 10 D-72076 Tübingen Germany
  
  

• Journal Foundations of Computational Mathematics
• Online ISSN 1615-3383
• Print ISSN 1615-3375

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