Electron. J. Diff. Equ., Vol. 2013 (2013), No. 40, pp. 1-20.

A step-like approximation and a new numerical schema for the Korteweg-de Vries equation in the soliton region

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
Odile Bastille
Department of Mathematics and Statistics
University of Alaska Fairbanks
PO Box 756660, Fairbanks, AK 99775, USA
email: orbastille@alaska.edu
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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