Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 15, pp. 1-21.

Title: Structured matrix numerical solution of the nonlinear schrodinger
       equation by the inverse scattering transform
   
Authors: Antonio Arico      (Univ. di Cagliari, Italy)
         Cornelis van der Mee (Univ. di Cagliari, Italy)
	 Sebastiano Seatzu  (Univ. di Cagliari, Italy)

Abstract:
  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.
 
Submitted December 23, 2008. Published January 13, 2009.
Math Subject Classifications: 35Q55, 65M32, 45D05.
Key Words: Nonlinear Schrodinger  equation; structured matrices;
           inverse scattering transform; numerical computation.