Lie and conditional symmetries of the three-component diffusive Lotka - Volterra system

Abstract

Lie and Q-conditional symmetries of the classical three-component diffusive Lotka - Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component non-linear reaction-diffusion system are constructed for the first time. An example of non-Lie symmetry reduction for solving a biologically motivated problem is presented.

References in corpus (4)

• Conditional Lie-Bäcklund symmetry and reduction of evolution equations.
• Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system
• On nonlinear partial differential equations with an infinite-dimensional conditional symmetry
• Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems

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