Lie and conditional symmetries of the three-component diffusive Lotka -   Volterra system
  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. 
Roman Cherniha and Vasyl' Davydovych
math-ph math.MP nlin.SI