Symmetry reductions of a (2 + 1)‐dimensional Keller–Segel model

Abstract

In this work, symmetry groups are used to determine symmetry reductions of a (2 + 1)‐dimensional Keller–Segel system depending on two arbitrary functions. We show that the point symmetries of the considered Keller–Segel system comprise an infinite‐dimensional Lie algebra which involves three arbitrary functions. By way of example, we have used these point symmetries to reduce straightaway the given system of second‐order partial differential equations to a system of second‐order ordinary differential equations. Moreover, we are allowed to substitute one of the dependent variables from one of the equations into the other, leading to an equivalent fourth‐order nonlinear ordinary differential equation. This equation is reduced through the use of solvable symmetry subalgebras, and some exact solutions are obtained for a particular case.

Special Issue “CMMSE 2020” in Mathematical Methods in the Applied Sciences (MMA)

“…The articles [3, 4] and [5] present important advances in mathematical methods applied to biology and physics . The first deals with the Keller‐Segel model, a mathematical model used to describe the movement of biological organisms.…”