The nonlinear wave structure of small-amplitude dust ion-acoustic cnoidal and solitary
waves are investigated in a five-component plasma consisting of positive proton beam from
solar wind, positive ion fluid, two electrons population, one of them from the solar wind
and stationary positive dust grains. The physical parameters in the system such as, the
temperature ratio of proton beam and positive ion, magnetic field and streaming velocity
of the beam plays the dominant role in the profile of the amplitude and the width of the
wave. Using the reductive perturbation theory, the basic set of equations is reduced to
a Zakharov–Kuznetsov equation. The latter has been solved using the Painlev ́e analysis
to obtain a set of analytical solutions, which reflects the possibility of the propagation
of various nonlinear structures. The solutions of Zakharov–Kuznetsov equation present a
positive potential, which corresponds to a compressive wave profile. The findings of this
investigation are used to interpret the electrostatic cnoidal and solitary waves that may
be observed in the Jupiter ionosphere.