It is well known that soliton equations such as the Korteweg–de Vries equation are members of inﬁnite sequences of PDEs known as hierarchies. Here we consider inﬁnite sequences of ODEs associated with the Painlevé equations. We review methods of constructing such hierarchies, speciﬁcally the second Painlevé hierarchy, as reductions of PDE hierarchies. We also show that in the large-parameter limit, the solutions of the second Painlevé hierarchy are given by the periodic solutions of the stationary KdV hierarchy.
Cite this article
Nalini Joshi, The Second Painlevé Hierarchy and the Stationary KdV Hierarchy. Publ. Res. Inst. Math. Sci. 40 (2004), no. 3, pp. 1039–1061DOI 10.2977/PRIMS/1145475502