  We present several analytical solutions of BPS vortices and monopoles in the
generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively.
These models have recently been extensively studied and several exact solutions
have already been obtained in \cite{Casana:2014qfa, Casana:2013lna}. In each
theory, the dynamics is controlled by the additional two positive
scalar-field-dependent functions, $f(|\phi|)$ and $w(|\phi|)$. For the case of
vortices, we work in the ordinary symmetry-breaking Higgs potential, while for
the case of monopoles we have the ordinary condition of the Prasad-Sommerfield
limit. Our results generalize that of exact solutions found previously. We also
present solutions for BPS vortices with higher winding number. These solutions
suffer from the condition that $w(|\phi|)$ has negative value at some finite
range of $r$, but we argue that since it satisfies the weaker positive-value
conditions then the corresponding energy density is still positive-definite
and, thus, they are acceptable BPS solutions.
