A diversity of physical phenomena is modelled by systems of nonlinear differential
equations not, in general, amenable to exact solution. However, in certain
cases, exploitation of hidden symmetries in the nonlinear models can lead to solutions
and reduction to canonical systems. Invariance under Lie groups and/or
Bäcklund transformations are two pivotal methods in this regard. [Continues.]
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.
A studentship from LUT and an ORS award are acknowledged.