Higher order Painleve equations and their symmetries via reductions of a class of integrable models

Abstract

Higher order Painleve equations and their symmetry transformations belonging to extended affine Weyl groups A(n)((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 Painleve V equation and its Backlund symmetry is obtained through a self-similarity limit of a generalized KdV hierarchy from Aratyn et al (1995 Int. J. Mod. Phys. A 10 2537).