Non-linear reaction-diffusion systems with variable diffusivities: Lie symmetries, ansätze and exact solutions

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Abstract

This work first considers the classical Lie symmetry analysis of a class of systems of two quasilinear reaction-diffusion equations having variable diffusivities. Subsequently, non-Lie reductions to systems of first order ordinary differential equations are obtained for a subclass of these systems. In particular, families of exact solutions of a diffusive Lotka-Volterra type system are constructed. © 2004 Elsevier Inc. All rights reserved.

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Cherniha, R., & King, J. R. (2005). Non-linear reaction-diffusion systems with variable diffusivities: Lie symmetries, ansätze and exact solutions. Journal of Mathematical Analysis and Applications, 308(1), 11–35. https://doi.org/10.1016/j.jmaa.2004.10.034

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