GEOMETRIC INVESTIGATION OF NONLINEAR REACTION-DIFFUSION-CONVECTION EQUATIONS: FISHER EQUATION AND ITS EXTENSIONS
This paper presents a comprehensive geometric study on the results obtained from the exact solution of the nonlinear reaction-diffusion-convection equations. The proposed equations are one of the most commonly used equations in the field of biology and chemistry, biochemistry, ecology, medicine, economics etc. Using the advanced concepts of the geometry one can well answer the reaction-diffusion-convection equations. These methods have on based the concepts of Riemannian manifolds including Lie symmetries and non-Lie symmetries as a generalization of Lie symmetries (Q-conditional symmetries in this paper). Nonlinear equations of reaction-diffusion- convection which investigated are nonlinear Fisher equation, the natural generalization of Fisher equation, Murray equation.
nonlinear Fisher equation, Murray equation, Lie symmetries, Q‑conditional symmetries.
Received: February 10, 2021; Accepted: March 6, 2021; Published: April 27, 2021
How to cite this article: Atefeh Hasan-Zadeh, Geometric investigation of nonlinear reaction-diffusion-convection equations: fisher equation and its extensions, Advances in Differential Equations and Control Processes 24(2) (2021), 145-151. DOI: 10.17654/DE024020145
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