Higher Order Painlevé Equations and their Symmetries via Reductions of a Class of Integrable Models

Higher order Painlevé equations and their symmetry transformations belonging to extended affine Weyl groups An(1) are obtained through a self-similarity limit of a class of pseudo-differential Lax hierarchies with symmetry inherited from the underlying generalized Volterra lattice structure. In particular, an explicit example of the Painlevé V equation and its Bäcklund symmetry is obtained through a self-similarity limit of a generalized KdV hierarchy from reference [3].