On Modulated NLS-Ermakov Systems

Modulated Kepler-Ermakov triads. Integrable Hamiltonian structure and parametrisation

“…The class of involutory transformations I * is of a type originally applied in [9] to autonomise the standard Ermakov-Ray-Reid system corresponding to H = 0 in (5). Application has been subsequently been made to reduce Ermakov-modulated nonlinear Schrödinger models [10][11][12][13] and coupled solitonic sine-Gordon, Demoulin and Manakov systems [14] to their integrable counterparts. In [15,16] modulated systems have been recently arisen in the analysis of heterogeneous moving boundary problems such as model the transport of liquids through a porous medium such as soil.…”

Moving boundary problems for a canonical member of the WKI inverse scattering scheme: conjugation of a reciprocal and Möbius transformation

“…Like soliton systems they admit nonlinear superposition principles [75] and underlying linear structure [72] albeit of another kind. Nonlinear Schrödinger systems with Ermakov-type modulation as originally introduced in [76] have subsequently been investigated in [77][78][79].…”