Non-Isospectral 1+1 Hierarchies Arising from a Camassa Holm Hierarchy in 2+1 Dimensions

The non-isospectral problem (Lax pair) associated with a hierarchy in 2+1 dimensions that generalizes the well known Camassa-Holm is presented. Here, we have investigated non-classical Lie symmetries of this Lax pair when spectral parameter considered as field. These can be written terms five arbitrary constants and three functions. Different similarity reductions these been derived. Of particular interest are reduced hierarchies whose $1+1$ also non-isospectral.