Symmetry reductions of a 2+1 Lax pair

In this Letter we present the reductions arising from the classical Lie symmetries of a Lax pair in 2+1 dimensions. We obtain several interesting reductions and prove that, by analyzing not only a PDE but also its associated linear problem, it is possible to obtain the reduction of the PDE together with the reduced Lax pair. Specially relevant is the fact that the spectral parameter in 1+1 dimensions appears as a natural consequence of the reduction itself and is related to the symmetry of the 2+1 eigenfunction.