Abstract: By using the theory of planar dynamical systems to the ion acoustic plasma equations, we obtain the existence of the solutions of the smooth and non-smooth solitary waves and the uncountably infinite smooth and non-smooth periodic waves. Under the given parametric conditions, we present the sufficient conditions to guarantee the exis-tence of the above solutions.

Key words: solitary traveling wave solution, periodic traveling wave solution, smooth-ness of waves, ion acoustic plasma equations