School of Mathematical Sciences

Symmetries and exact solutions of the diffusive Lotka-Volterra systems

Thursday 25th May (15:00) - Thursday 8th June 2023 (16:00)
Event Convenor Contact:
Speaker's Name: Roman Cherniha
Speaker's Affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, and UoN
Speaker's Research Theme(s): Fluid mechanics,
This talk is devoted to symmetries and methods of integration of the classical Lotka-Volterra systems with diffusion. Lie and conditional (nonclassical) symmetries are identified and used for constructing exact solutions, which satisfy typical boundary conditions and describe different scenario of population (cell, tumour) evolution. In particular, several highly nontrivial exact solutions, including traveling fronts, are found, their properties are identified and a biological interpretation is discussed. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate and numerical methods for solving boundary value problems related to the diffusive Lotka-Volterra systems. Because the Lotka-Volterra type systems are used for mathematical modeling of an enormous variety of processes in ecology, biology, medicine, physics and chemistry, the talk could be interesting not only for specialists in PDEs but also scholars from other branches of science. The talk is based on the results obtained in collaboration with Dr. Davydovych (Institute of Mathematics, Kyiv) and published in several recent papers including the review ‘Construction and application of exact solutions of the diffusive Lotka--Volterra system: A review and new results.’ Commun. in Nonlin. Sci. and Num. Simul. Vol.113(2022), 106579.

Venue: Life Sciences B1
Online Conference Link:

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

For all enquiries please visit: