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arXiv · 2610.34129

Lie symmetry analysis of the Saint--Venant equations with variable bottom

Faruk Güngör·Cihangir Özemir·Pedro J. Torres
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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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Faruk Güngör, Cihangir Özemir, Pedro J. Torres. 2026-10-25. Lie symmetry analysis of the Saint--Venant equations with variable bottom. https://arxiv.org/abs/2610.34129

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