Integrable 1+1 dimensional hierarchies arising from reduction of a non-isospectral problem in 2+1 dimensions

摘要

This work presents a classical Lie point symmetry analysis of a two-component, non-isospectral Lax pair of a hierarchy of partial differential equations in 2+1 dimensions, which can be considered as a modified version of the Camassa–Holm hierarchy in 2+1 dimensions. A classification of reductions for this spectral problem is performed. Non-isospectral reductions in 1+1 dimensions are considered of remarkable interest.