On integrable Ermakov–Painlevé IV systems

Abstract

Novel hybrid Ermakov-Painlevé IV systems are introduced and an associated Ermakov invariant is used in establishing their integrability. Bäcklund transformations are then employed to generate classes of exact solutions via the linked canonical Painlevé IV equation.

On Modulated NLS-Ermakov Systems

“…The diversity of Bäcklund and Schlesinger-type transformations admitted by Painlevë IV has been catalogued in the comprehensive work of [4]. With regard to the positivity constraint on Σ, the iterated action of a Bäcklund transformation on a seed bound state solution set down in [5] has recently been used in [42] to generate an infinite sequence of bound state solutions Σ n of Painlevé IV. These Σ n have regions separated by zeros on which they are positive.…”