  A class of nonlinear Schr\"odinger equations involving a triad of power law
terms together with a de Broglie-Bohm potential is shown to admit symmetry
reduction to a hybrid Ermakov-Painlev\'e II equation which is linked, in turn,
to the integrable Painlev\'e XXXIV equation. A nonlinear Schr\"odinger
encapsulation of a Korteweg-type capillary system is thereby used in the
isolation of such a Ermakov-Painlev\'e II reduction valid for a multi-parameter
class of free energy functions. Iterated application of a B\"acklund
transformation then allows the construction of novel classes of exact solutions
of the nonlinear capillarity system in terms of Yablonskii-Vorob'ev polynomials
or classical Airy functions. A Painlev\'e XXXIV equation is derived for the
density in the capillarity system and seen to correspond to the symmetry
reduction of its Bernoulli integral of motion.
