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.