Symmetry and Integrability of Equations of Mathematical Physics − 2011

Alexander Shapovalov (Tomsk State University, Tomsk, Russia)
Andrey Trifonov (National Research Tomsk Polytechic University, Tomsk, Russia)

Symmetries of integro-differential reaction-diffusion equation with quadratic operator

Symmetries of the Fisher-Kolmogorov-Petrovski-Piskunov (FKPP) equation with nonlocal competition loses are considered in the framework of the semiclassical approximation. The nonlocal FKPP equation is reduced to a PDE with quadratic operator in coordinates and derivatives and including nonlocal terms in the form of moments of the equation solution. A dynamic system of ODEs, the Einstein-Ehrenfest (EE) system, describing evolution of the moments is obtained. Examples of symmetries of the joint system consisting of the reduced FKPP equation and the EE system, a symmetry group, and a group invariant solution are found.

This is joint work with E.A. Levchenko (National Research Tomsk Polytechic University, Tomsk, Russia).