  We have studied the existence of self-dual solitonic solutions in a
generalization of the Abelian Chern-Simons-Higgs model. Such a generalization
introduces two different nonnegative functions, $\omega_1(|\phi|)$ and
$\omega(|\phi|)$, which split the kinetic term of the Higgs field -
$|D_\mu\phi|^2 \rightarrow\omega_1 (|\phi|)|D_0\phi|^2-\omega(|\phi|)
|D_k\phi|^2$ - breaking explicitly the Lorentz covariance. We have shown that a
clean implementation of the Bogomolnyi procedure only can be implemented
whether $\omega(|\phi|) \propto \beta |\phi|^{2\beta-2}$ with $\beta\geq 1$.
The self-dual or Bogomolnyi equations produce an infinity number of soliton
solutions by choosing conveniently the generalizing function $\omega_1(|\phi|)$
which must be able to provide a finite magnetic field. Also, we have shown that
by properly choosing the generalizing functions it is possible to reproduce the
Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs
models. Finally, some new self-dual $|\phi|^6$-vortex solutions have been
analyzed both from theoretical and numerical point of view.
