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>> 30.10.04

Literature review (iv)
This is the fourth part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. The classification of symmetries, linearising transformations and invariant soltuions formed a great deal of the research effort once symmetry methods were reclaimed from pure mathematicians. Ovsiannikov paid much attention to constructing group-invariant solutions, whilst a reference book containing the symmetries etc. of many PDEs was developed by Ibragimov. Thus, in its classical... {>>}

>> 29.10.04

Literature review (iii)
This is the third part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. Once the symmetry group of a given differential equation has been calculated there are many possible applications. For ordinary differential equations (ODEs), invariance under a one-parameter Lie group of transformations means that the order of the equation can be reduced by one, complete with one quadrature. In the case of a first-order... {>>}

>> 28.10.04

Literature review (ii)
This is the second part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. A symmetry of a differential equation is a transformation that maps solutions of the equation to other solutions; a Lie symmetry group of transformations is a group of transformations (which depend upon continuous parameters) that map any solution of the equation to another solution. These symmetries, examples of which are translations, rotations... {>>}

>> 27.10.04

Literature review (i)
This is the first part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. The reproduction of it here is provided for the interested reader, as a reference for others involved in the area of symmetry analysis and as an easily locatable reference for myself. There are nine sections (all of which will be linked to in each section) and a bibliography will be made available at a later point. Towards the end of the 19th century,... {>>}

>> 26.10.04

Completed annual review
The customary silence of the PhD diary will not have worried many people so we'll just pretend that it didn't happen and move on. The annual report was completed some time ago now and has been accepted by all the people it needed to be. I was pleased with the result, which included a detailed introduction to the area of symmetry methods and in particular the use of symmetry methods in the solution of initial- and boundary-value problems. I will post the literature review over the coming days in a... {>>}