  The NJL-jet model provides a sound framework for calculating the
fragmentation func- tions in an effective chiral quark theory, where the
momentum and isospin sum rules are satisfied without the introduction of ad hoc
parameters [1]. Earlier studies of the pion fragmentation func- tions using the
Nambu-Jona-Lasinio (NJL) model within this framework showed good qualitative
agreement with the empirical parameterizations. Here we extend the NJL-jet
model by including the strange quark. The corrections to the pion fragmentation
function and corresponding kaon fragmen- tation functions are calculated using
the elementary quark to quark-meson fragmentation functions from NJL. The
results for the kaon fragmentation function exhibit a qualitative agreement
with the empirical parameterizations, while the unfavored strange quark
fragmentation to pions is shown to be of the same order of magnitude as the
unfavored light quark's. The results of these studies are expected to provide
important guidance for the analysis of a large variety of semi-inclusive data.
