  By employing a self-similar, two-fluid MHD model in a cylindrical geometry,
we study the features of nonlinear ion-acoustic (IA) waves which propagate in
the direction of external magnetic field lines in space plasmas. Numerical
calculations not only expose the well-known three shapes of nonlinear
structures (sinusoidal, sawtooth, and spiky or bipolar) which are observed by
numerous satellites and simulated by models in a Cartesian geometry, but also
illustrate new results, such as, two reversely propagating nonlinear waves,
density dips and humps, diverging and converging electric shocks, etc. A case
study on Cluster satellite data is also introduced.
