  A non-isospectral linear problem for an integrable 2+1 generalization of the
non linear Schr\"odinger equation, which includes dispersive terms of third and
fourth order, is presented. The classical symmetries of the Lax pair and the
related reductions are carefully studied. We obtain several reductions of the
Lax pair that yield in some cases non-isospectral problems in 1+1 dimensions.
