Starting from the scattering data, the initial-value problem for the focusing nonlinear Schrödinger equation is solved numerically by following the path of the inverse scattering transform. The numerical results of an extensive experimentation suggest that: (a) our method is very effective, whenever the scattering data are analytically known; (b) the split-step Fourier method is not really effective if the exact solution is not smooth enough.
Numerical solution of the nonlinear Schrödinger equation, starting from the scattering data
RODRIGUEZ, GIUSEPPE;
2011-01-01
Abstract
Starting from the scattering data, the initial-value problem for the focusing nonlinear Schrödinger equation is solved numerically by following the path of the inverse scattering transform. The numerical results of an extensive experimentation suggest that: (a) our method is very effective, whenever the scattering data are analytically known; (b) the split-step Fourier method is not really effective if the exact solution is not smooth enough.
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