Whitham equations and phase shifts for the Korteweg-deVries equation
arXiv:2006.03924 · doi:10.1098/rspa.2020.0300
Abstract
The semi-classical Korteweg-deVries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis Whitham theory is constructed to higher order. This allows the order one phase and the complete leading order solution to be obtained; the results are confirmed by extensive numerical calculations.
25 pages, 5 figures, a shorter version is accepted for publication in Proc. Roy. Soc. A