Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system
Roman Cherniha, Vasyl' Davydovych
TL;DR
This paper classifies Q-conditional symmetries of the one-dimensional Lotka-Volterra system, constructs explicit symmetries, derives new exact solutions via reduction to ODEs, and discusses their biological relevance.
Contribution
It provides a complete description of Q-conditional symmetries for the system and introduces new exact solutions with biological interpretations.
Findings
Complete classification of Q-conditional symmetries.
Construction of explicit symmetries and reduction to ODEs.
New exact solutions with biological significance.
Abstract
Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ans\"atze to reduce the classical Lotka-Volterra systems with correctly-specified coefficients to ODE systems and examples of new exact solutions are found. A possible biological interpretation of some exact solutions is presented.
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