In this work we emphasise the use of singularity analysis in obtaining
analytic solutions for equations for which standard Lie point symmetry
analysis fails to make any lucid decision. We study the
higher-dimensional Kadomtsev-Petviashvili, Boussinesq and
Kaup-Kupershmidt Equations in a more general sense. With higher-order
equations there can be a commensurate number of resonances and, when
consistency for the full equation is examined, at each resonance the
constant of integration is supposed to vanish from the expression so
that it remains arbitrary, but if there is an instance of this not
happening, the consistency can be partially established by giving the
oﬀending constant the value from the deﬁning equation. If consistency is
otherwise not compromised, the equation can be said to be partially
integrable, ie, integrable on a surface of the complex space.
Furthermore we propose an approach which is meant to magnify the scope
of singularity analysis for equations admitting higher values for
resonances or positive leading-order exponent.