Hybrid Ermakov-Painlevé IV Systems

Colin Rogers
2014 Journal of Nonlinear Mathematical Physics  
Ermakov-Painlevé IV coupled systems are introduced and associated Ermakov-type invariants isolated. These invariants are used to obtain systematic reduction of the system in terms of the canonical Painlevé IV equation. The procedure is applied to a Ermakov-Painlevé IV symmetry reduction of a coupled derivative resonant nonlinear Schrödinger triad incorporating de Broglie-Bohm potential terms. where, in the above, the dot indicates a derivative with respect to the independent variable t.
more » ... ntly 2+1-dimensional versions of (1.1) were introduced in [47] while extensions to arbitrary order and dimension which preserve the characteristic invariant were presented in [59]. Multicomponent Ermakov-Ray-Reid systems were introduced in a hydrodynamics context in [42] via a symmetry reduction of a 2+1-dimensional multi-layer fluid model. Moreover, sequences of twocomponent Ermakov-Ray-Reid systems were shown therein to be linked via Darboux transformations. Discretisation aspects of particular Ermakov-type equations have been investigated in [55,57].
doi:10.1080/14029251.2014.975531 fatcat:326plunoujbxxlwvcxekbvhq54