Jason Baggett, Odile Bastille, Alexei Rybkin
Abstract:
We discuss a numerical schema for solving the initial value problem for
the Korteweg-de Vries equation in the soliton region which is based
on a new method of evaluation of bound state data. Using a
step-like approximation of the initial profile and a fragmentation principle
for the scattering data, we obtain an explicit procedure for
computing the bound state data. Our method demonstrates an improved accuracy
on discontinuous initial data.
We also discuss some generalizations of this algorithm and how it might be
improved by using Haar and other wavelets.
Submitted September 27, 2011. Published February 4, 2013.
Math Subject Classifications: 35P25, 35Q53, 37K15, 37K10, 37K40, 42C40, 65N25.
Key Words: KdV equation; Haar wavelets; potential fragmentation;
inverse scattering transform.
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Jason Baggett Department of Mathematics and Statistics University of Alaska Fairbanks PO Box 756660, Fairbanks, AK 99775, USA email: jabaggett@alaska.edu |
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Odile Bastille Department of Mathematics and Statistics University of Alaska Fairbanks PO Box 756660, Fairbanks, AK 99775, USA email: orbastille@alaska.edu |
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Alexei Rybkin Department of Mathematics and Statistics University of Alaska Fairbanks PO Box 756660, Fairbanks, AK 99775, USA email: arybkin@alaska.edu |
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