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