Data Analysis and Reduction Using Stationary Solutions of the NLS Equation

Date Added: Aug 2009
Format: PDF

This paper demonstrates that the stationary solutions of the Nonlinear Schrodinger Equation (NLS) can be used as an orthonormal basis for the square integrable functions with periodic boundary conditions. This allows one to use these solutions in much the same way as regular Fourier modes or other basis sets. For instance, one shows the applicability of the NLS basis set for doing data analysis, and as a means for obtaining reduced models. Using a variety of examples, one shows that working with the NLS basis set is advantageous over working with the set of Fourier modes, which it contains as a special case.