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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Titolo: Structured matrix numerical solution of the nonlinear Schrodinger equation by the inverse scattering transform
Autori: 
VAN DER MEE, CORNELIS VICTOR MARIA
mostra contributor esterni 
Data di pubblicazione: 2009
Rivista: 
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS  
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.
Handle: http://hdl.handle.net/11584/19037
Tipologia:1.1 Articolo in rivista

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http://hdl.handle.net/11584/19037
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