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

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.