PreprintCC BY 4.0arXiv
Bore wave solutions to the viscous Saint-Venant system with capillarity
Abstract
We study a traveling wave formulation of the viscous Saint-Venant system in one spatial dimension with capillarity, which can be reduced to an equivalent nonlinear third order ODE. We construct heteroclinic orbits for small positive capillarity, for arbitrary positive capillarity under an explicit small Froude number condition, and in a small-amplitude regime away from the critical Froude number. These then give rise to smooth traveling bore wave solutions to the viscous Saint-Venant system.
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BibTeX
@misc{meng2026bore,
title = {{Bore wave solutions to the viscous Saint-Venant system with capillarity}},
author = {Keming Meng and Ian Tice},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37879},
eprint = {2610.37879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37879},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bore wave solutions to the viscous Saint-Venant system with capillarity
AU - Keming Meng
AU - Ian Tice
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37879
UR - https://arxiv.org/abs/2610.37879
AB - We study a traveling wave formulation of the viscous Saint-Venant system in one spatial dimension with capillarity, which can be reduced to an equivalent nonlinear third order ODE. We construct heteroclinic orbits for small positive capillarity, for arbitrary positive capillarity under an explicit small Froude number condition, and in a small-amplitude regime away from the critical Froude number. These then give rise to smooth traveling bore wave solutions to the viscous Saint-Venant system.
ER -