Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system

@article{Cherniha2011ConditionalSA,
  title={Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system},
  author={Roman Cherniha and Vasyl' Davydovych},
  journal={Mathematical and Computer Modelling},
  year={2011},
  volume={54},
  pages={1238-1251}
}
Q -conditional symmetries of the classical diffusive 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 ansatz to reduce the diffusive 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. © 2011 Elsevier Ltd. All rights reserved. 

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