  The behaviour of pseudoscalar mesons within the SU(3)PNJL-like models is
considered for finite T and $\mu_B$. We compare the pole approximation
(Breit-Wigner) with the Beth-Uhlenbeck approach. We evaluate the $K/\pi$ ratios
along the phase transition line in the T-$\mu_B$ plane with constant and
$T/\mu_B$-dependent pion and strange quark chemical potentials. Using the
model, we can show that the splitting of kaon and anti-kaon masses appears as a
result of introduction of density and this explains the difference in the
$K^+/\pi^+$ ratio and $K^-/\pi^-$ ratio at low $\sqrt{s_{NN}}$ and their
tendency to the same value at high $\sqrt{s_{NN}}$. A sharp "horn" effect in
the $K^+/\pi^+$ ratio is explained by the enhanced pion production which can be
described by occurrence of a nonequilibrium pion chemical potential of the
order of the pion mass. We elucidate that the horn effect is not related to the
existence of a critical endpoint in the QCD phase diagram.
