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

ANTONIO ARICO;VAN DER MEE, CORNELIS VICTOR MARIA;SEBASTIANO SEATZU

2009-01-01

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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.