Generalized Qiao hierarchy in 2+1 dimensions: Reciprocal transformations, spectral problem and non-isospectrality

A new integrable 2+1 hierarchy that generalizes the 1+1 Qiao hierarchy is presented. A reciprocal transformation is defined such that the independent x-variable is considered as a dependent field. The hierarchy transforms into n copies of an equation that has a two component non-isospectral Lax pair. Coming back to the original variables, by inverting the reciprocal transformation we obtain a two component spectral problem for the 2+1 hierarchy. Actually, this spectral problem is non-isospectral.