Electron. J. Diff. Eqns., Vol. 2009(2009), No. 15, pp. 1-21.

Structured matrix numerical solution of the nonlinear schrodinger equation by the inverse scattering transform

Antonio Arico, Cornelis van der Mee, Sebastiano Seatzu

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.

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Antonio Aricò
Dip. Matematica e Informatica, Università di Cagliari
Viale Merello 92, 09123 Cagliari, Italy
email: arico@unica.it
Cornelis van der Mee
Dip. Matematica e Informatica, Università di Cagliari
Viale Merello 92, 09123 Cagliari, Italy
email: cornelis@krein.unica.it
Sebastiano Seatzu
Dip. Matematica e Informatica, Università di Cagliari
Viale Merello 92, 09123 Cagliari, Italy
email: seatzu@unica.it

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