  The nonlinear propagation of heavy-ion-acoustic (HIA) waves (HIAWs) in a four
component multi-ion plasma (containing inertial heavy negative ions and light
positive ions, as well as inertialess nonextensive electrons and positrons) has
been theoretically investigated. The nonlinear Schr\"{o}dinger (NLS) equation
is derived by employing the reductive perturbation method. It is found that the
NLS equation leads to the modulational instability (MI) of HIAWs, and to the
formation of HIA rogue waves (HIARWs), which are due to the effects of
nonlinearity and dispersion in the propagation of HIAWs. The conditions for MI
of HIAWs, and the basic properties of the generated HIARWs are identified. It
is observed that the striking features (viz. instability criteria, growth rate
of MI, amplitude and width of HIARWs, etc.) of the HIAWs are significantly
modified by effects of nonextensivity of electrons and positrons, ratio of
light positive ion mass to heavy negative ion mass, ratio of electron number
density to light positive ion number density, and ratio of electron temperature
to positron temperature, etc. The relevancy of our present investigation to the
observations in the space (viz. cometary comae and earth's ionosphere) and
laboratory (laser plasma interaction experimental devices) plasmas is pointed
out.
