Higher order symmetries of the (2+1) heat equation with a source term.

摘要

Symmetry analysis has played an important role in obtaining exact solutions of partial differential equations. A particular class of equations that has benefited from this type of analysis has been reaction-diffusion equations. Recently it was shown that the symmetries of a (2+1) diffusion equation with a quadratic source term are special as they have an extremely rich structure. This thesis further investigates this equation as we determine whether quadratic source terms remain special when moving to higher order symmetries.