Whitham equations and phase shifts for the Korteweg–de Vries equation-Reference-Cited by-同舟云学术

Whitham equations and phase shifts for the Korteweg–de Vries equation

Published:2020-08 Issue:2240 Volume:476 Page:20200300
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Ablowitz Mark J.¹,Cole Justin T.¹,Rumanov Igor¹^ORCID

Affiliation:

1. Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA

Abstract

The semi-classical Korteweg–de Vries 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 the 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.

Funder

National Science Foundation

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2020.0300

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