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Lie Symmetry Techniques for Partial Differential Equations

By Maureen Edwards (UOW) and Bronwyn Hajek (UniSA)

9—10 May, 2019

Venue: SR202, SR Building, Callaghan Campus



Notices

Technical requirements (updated)

Please note the technical requirements for the workshop, listed below. Instructions for installation have been added (30 April).

Registration

Registration is now open through Eventbrite.

Workshop times

The workshop will run 9-5 on Thursday (9th May) and 9-12 on Friday (10th May).

Schedule

The schedule has been added below, or you can download a PDF version.

About the workshop

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.

Venue

The venue for the workshop is room SR202 in the SR building, at the University of Newcastle's Callaghan Campus.

Workshop Overview

The workshop will cover

Registration

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.

Prerequisites

Resources

These will be distributed to participants prior to the workshop.

Technical requirements

Workshop participants should bring a laptop with Maple, and with Reduce and Dimsym installed.

Installation instructionsClick here to download the instructions for installing these packages (308 KB PDF file).

Schedule Schedule

Thursday 9th May

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:

Friday 10th May

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.

Biographies

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.

Contact Information

If you have any questions, please contact

Juliane Turner

Juliane.Turner@newcastle.edu.au

Telephone: (02) 492 15483