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Lie symmetry analysis of the Saint--Venant equations with variable bottom
Abstract
The aim of this paper is to apply Lie-symmetry methods to the one-dimensional Saint--Venant shallow-water equations over variable bottom topography. We classify the bottom profiles that admit symmetry extensions, derive similarity reductions to ordinary differential equations, and analyze selected reduced systems. In particular, heteroclinic trajectories yield physically meaningful self-similar solutions describing the draining and filling of water over a quadratic bottom with a fixed shoreline.
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BibTeX
@misc{gungor2026symmetry,
title = {{Lie symmetry analysis of the Saint--Venant equations with variable bottom}},
author = {Faruk Güngör and Cihangir Özemir and Pedro J. Torres},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34129},
eprint = {2610.34129},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34129},
}
RIS
TY - UNPB
TI - Lie symmetry analysis of the Saint--Venant equations with variable bottom
AU - Faruk Güngör
AU - Cihangir Özemir
AU - Pedro J. Torres
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34129
UR - https://arxiv.org/abs/2610.34129
AB - The aim of this paper is to apply Lie-symmetry methods to the one-dimensional Saint--Venant shallow-water equations over variable bottom topography. We classify the bottom profiles that admit symmetry extensions, derive similarity reductions to ordinary differential equations, and analyze selected reduced systems. In particular, heteroclinic trajectories yield physically meaningful self-similar solutions describing the draining and filling of water over a quadratic bottom with a fixed shoreline.
ER -