Publications de l'Institut Mathématique, Nouvelle Série Vol. 96[110], pp. 125–141 (2014) 

EMERGING PROBLEMS IN APPROXIMATION THEORY FOR THE NUMERICAL SOLUTION OF THE NONLINEAR SCHRÖDINGER EQUATIONL. Fermo, C. Van der Mee, and S. SeatzuDepartment of Mathematics and Computer Science, University of Cagliari, Cagliari, ItalyAbstract: We present some open problems pertaining to the approximation theory involved in the solution of the Nonlinear Schrödinger (NLS) equation. For this important equation, any Initial Value Problem (IVP) can be theoretically solved by the Inverse Scattering Transform (IST) technique whose main steps involve the solution of Volterra equations with structured kernels on unbounded domains, the solution of Fredholm integral equations and the identification of coefficients and parameters of monomialexponential sums. The aim of the paper is twofold: propose a method for solving the above mentioned problems under particular hypothesis; arise interest in the issues illustrated to achieve an effective method for solving the problem under more general assumptions Classification (MSC2000): 41A46, 65R20, 35P25 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 30 Oct 2014. This page was last modified: 24 Nov 2014.
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