On non-existence of bifurcations in one-dimensional Bratu equation
Dynamical Systems
2026-05-29 v2
Abstract
In this paper, we revisit the classical problem of Bratu differential equation in one-dimension. While it is known that the finite difference discretized form of continuous Bratu equation gives rise to spurious bifurcations, we show that spurious bifurcation points exist even when the finite element approach is employed. We then present an analytical proof demonstrating that there are no bifurcations when the continuous Bratu equation is considered.
Keywords
Cite
@article{arxiv.2512.05141,
title = {On non-existence of bifurcations in one-dimensional Bratu equation},
author = {Shrinidhi S. Pandurangi and Utkarsh S. Nikam},
journal= {arXiv preprint arXiv:2512.05141},
year = {2026}
}