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 arbitra...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-10, Vol.46 (15), p.15972-15981
Main Authors: de la Rosa, Rafael, Garrido, Tamra Maria, Bruzón, Maria Santos
Format: Article
Language:English
Subjects:
Dependent variables
Exact solutions
Lie groups
Nonlinear differential equations
Partial differential equations
Symmetry
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7330