Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 40, pp. 1-20.

Title: A step-like approximation and a new numerical schema
       for the Korteweg-de Vries equation in the soliton region
        
Authors: Jason Baggett  (Univ. of Alaska,  Fairbanks, AK, USA)
         Odile Bastille (Univ. of Alaska,  Fairbanks, AK, USA)
         Alexei Rybkin  (Univ. of Alaska,  Fairbanks, AK, USA)
        
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 04, 2013.
Math Subject Classifications: 35P25, 35Q53, 37K15, 37K10, 37K40, 42C40, 65N25.
Key Words: KdV equation; Haar wavelets; potential fragmentation;
           inverse scattering transform.