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.

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

VAN DER MEE, CORNELIS VICTOR MARIA;
2009

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/19037
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