Classical Lie symmetries and reductions of a nonisospectral Lax pair

The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries provides a set of reductions that give rise to different nontrivial spectral problems in 1+1 dimensions. The form in which the spectral parameter of the 1+1 Lax pair is introduced is carefully described.