Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 469, Issue 2149, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2012.0330
Keywords
Riemann-Hilbert problem; nonlinear Schrodinger equations; inverse scattering transform; boundary-value problems
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Funding
- National Science Foundation [NSF-DMS-1008001]
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We solve the focusing and defocusing nonlinear Schrodinger (NLS) equations numerically by implementing the inverse scattering transform. The computation of the scattering data and of the NLS solution are both spectrally convergent. Initial conditions in a suitable space are treated. Using the approach of Biondini & Bui, we numerically solve homogeneous Robin boundary-value problems on the half line. Finally, using recent theoretical developments in the numerical approximation of Riemann-Hilbert problems, we prove that, under mild assumptions, our method of approximating solutions to the NLS equations is uniformly accurate in their domain of definition.
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