Whitham equations and phase shifts for the Korteweg-deVries equation
Pattern Formation and Solitons
2021-03-17 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.2006.03924,
title = {Whitham equations and phase shifts for the Korteweg-deVries equation},
author = {Mark J. Ablowitz and Justin T. Cole and Igor Rumanov},
journal= {arXiv preprint arXiv:2006.03924},
year = {2021}
}
Comments
25 pages, 5 figures, a shorter version is accepted for publication in Proc. Roy. Soc. A