New conditional symmetries and exact solutions of reaction-diffusion systems with power diffusivities
Roman Cherniha, Oleksii Pliukhin
TL;DR
This paper introduces new Q-conditional symmetries for reaction-diffusion systems with power-law diffusivities, enabling reduction to ODEs and deriving exact solutions relevant to spatially inhomogeneous structures.
Contribution
It constructs novel Q-conditional symmetries for reaction-diffusion systems with power diffusivities, expanding the methods for finding exact solutions.
Findings
New Q-conditional symmetries are identified.
Reduction of PDEs to ODEs using non-Lie ansatze.
Examples of exact solutions related to inhomogeneous structures.
Abstract
A wide range of new Q-conditional symmetries for reaction-diffusion systems with power diffusivities are constructed. The relevant non-Lie ansatze to reduce the reaction-diffusion systems to ODE systems and examples of exact solutions are obtained. The relation of the solutions obtained with the development of spatially inhomogeneous structures is discussed.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Quantum chaos and dynamical systems · Nonlinear Dynamics and Pattern Formation