A Numerical Investigation of the Whitham Equation for Solitary Waves Propagating on Conducting Flows

Souza M.; Flamarion M.V.; Ribeiro-Jr R.; Gao T. · Quarterly Journal of Mechanics and Applied Mathematics (2026) · DOI: 10.1093/qjmam/hbag003

Resumen

Summary: We introduce the Whitham equation in the context of electrohydrodynamic (EHD) flows, which incorporates the nonlinearity of the Korteweg-de Vries (KdV) and the full linear dispersion relation associated with EHD effects, extending the classical Whitham approach to electrical regimes. This EHD extension will be referred to as the e-Whitham equation. To assess its performance, we conduct numerical simulations comparing the e-Whitham equation to the Korteweg-de Vries-Benjamin-Ono (KdV-BO) across various electric field strengths. We investigate travelling wave profiles, solitary wave collisions, and trapped wave phenomena. The numerical experiments demonstrate strong agreement with asymptotic predictions. The model reduces to the KdV-BO equation in the weakly dispersive regime, confirming its consistency with known asymptotics and ensuring accuracy where asymptotic models are valid. Its main novelty lies in extending the Whitham framework to EHD flows, making it suitable for exploring parameter regimes beyond the reach of KdV-BO. © The Author(s) 2026. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Instituciones: Pontificia Universidad Católica del Perú