Lie symmetry methods can be useful for constructing exact solutions to differential equations. In this workshop, we will show how to determine the symmetry properties of linear and nonlinear partial differential equations, and how to exploit these properties to reduce the order of the governing equation. The workshop will focus on developing an understanding of the nuances in finding the symmetry classification of classes of differential equations. Simple Maple algorithms will be used to generate and solve determining equations. The symmetry determination package Dimsym (in Reduce) will be demonstrated. An overview of more generalised symmetry methods will also be discussed.
The venue for the workshop is room SR202 in the SR building, at the University of Newcastle's Callaghan Campus.
The workshop will cover
Registration is now open through Eventbrite. Note that while there is no cost to attend, you will need to register to ensure a place at the workshop.
These will be distributed to participants prior to the workshop.
Workshop participants should bring a laptop with Maple, and with Reduce and Dimsym installed.
We will discuss one-parameter groups of transformations. We will work though a number of examples, demonstrating how to obtain the determining equations and how to solve them to find the relevant symmetry group. Examples include:
On the second day we will discuss how to use the symmetry groups found on the first day. In particular, we will look at examples including:
We will also give a brief introduction to generalised symmetries, including nonlocal symmetries, and nonclassical symmetries.
Dr Maureen Edwards
Maureen is a Senior Lecturer in applied mathematics at the University of Wollongong. Her research interests include the use of symmetry analysis for the construction of exact solutions of nonlinear differential equations, motivated by physical phenomena such as biological invasion and population dynamics.
Dr Bronwyn Hajek
Bronwyn is a Senior Lecturer in applied mathematics at the University of South Australia. Her research interests lie in the use of symmetry techniques to construct analytic solutions of nonlinear reaction-diffusion equations, particularly with application to problems in mathematical biology. She has also worked on problems in viscous flow and physical chemistry.
If you have any questions, please contact
Telephone: (02) 492 15483