Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows
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Date
2025
Authors
Cherniha, Roman
King, John
Journal Title
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Volume Title
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Abstract
A wide class of two-component evolution systems is constructed admitting an infinite-dimensional Lie algebra. Some examples of such systems that are relevant to reaction–diffusion systems with cross-diffusion are highlighted. It is shown that a nonlinear evolution system related to the Ricci flow on warped product manifold, which has been extensively studied by several authors, follows from the above-mentioned class as a very particular case. The Lie symmetry properties of this system and its natural generalization are identified and a wide range of exact solutions is constructed using the Lie symmetry obtained. Moreover, a
special case is identified when the system in question is reducible to the fast diffusion equation in one space dimension. Finally, another class of two-component evolution systems with an infinite-dimensional Lie symmetry that possess essentially different structures is presented.
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Keywords
exact solution, Lie symmetry, nonlinear PDE, Ricci flow, article
Citation
Cherniha R. M. Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows / R. Cherniha, J. R. King // Studies in Applied Mathematics. - 2025. - Vol. 153 (3). - Art. no. e12737. - Р. 1-17. - https://doi.org/10.1111/sapm.12737