%0 Journal Article
%T Structured matrix numerical solution of the nonlinear schrodinger equation by the inverse scattering transform
%A Antonio Arico
%A Cornelis van der Mee
%A Sebastiano Seatzu
%J Electronic Journal of Differential Equations
%D 2009
%I Texas State University
%X The initial-value problem for the focusing nonlinear Schrodinger (NLS) equation is solved numerically by following the various steps of the inverse scattering transform. Starting from the initial value of the solution, a Volterra integral equation is solved followed by three FFT to arrive at the reflection coefficient and initial Marchenko kernel. By convolution these initial data are propagated in time. Using structured-matrix techniques the time evolved Marchenko integral equation is solved to arrive at the solution to the NLS equation.
%K Nonlinear Schrodinger equation
%K structured matrices
%K inverse scattering transform
%K numerical computation
%U http://ejde.math.txstate.edu/Volumes/2009/15/abstr.html