Non-classical symmetries and invariant solutions of non-linear Dirac equations

We apply Lie and non-classical symmetry methods to partial differential equations in order to derive solutions of the non-linear Dirac equation corresponding to the Gross-Neveu model in d=(1+1) and d=(2+1) space-time dimensions. For each d, we first identify sub-algebras of the Poincaré-Lie algebra and for each such sub-algebra, we calculate the invariant solution. Non-classical symmetries are also determined and used to derive new solutions for the Gross-Neveu model.