
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 integrodifferential
reactiondiffusion equation with quadratic operator
Abstract:
Symmetries of the FisherKolmogorovPetrovskiPiskunov (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 EinsteinEhrenfest (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).

