New Conditional Symmetries and Exact Solutions of the Diffusive Two-Component Lotka–Volterra System

Abstract

The diffusive Lotka–Volterra system arising in an enormous number of mathematical models in biology, physics, ecology, chemistry and society is under study. New Q-conditional (nonclassical) symmetries are derived and applied to search for exact solutions in an explicit form. A family of exact solutions is examined in detail in order to provide an application for describing the competition of two species in population dynamics. The results obtained are compared with those published earlier as well.

Keywords

• diffusive Lotka–Volterra system
• nonclassical symmetry
• <i>Q</i>-conditional symmetry of the first type
• exact solution