Acoustic nonlinear periodic (cnoidal) waves and solitons in pair-ion plasmas

Electrostatic acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in unmagnetized pair-ion plasmas consisting of the same mass ion species with different temperatures. It is found that the temperature difference between negatively and positively charged ions appropriates the dispersion property to linear acoustic waves and this difference has a decisive role in nonlinear dynamics as well. Using a reductive perturbation method and appropriate boundary conditions the Korteweg-de Vries equation is derived. Both cnoidal wave and soliton solutions are discussed in detail. In the special case, it is revealed that the amplitude of a soliton may become larger than what is allowed by the nonlinear stationary wave theory, which is equal to the quantum tunneling by a particle through a potential barrier effect. The serious flaw in the results obtained for ion acoustic nonlinear periodic waves by Yadav et al (1995 Phys. Rev. E 52 3045) in two-electron temperature plasmas and Chawla and Misra (2010 Phys. Plasmas 17 102315) in electron-positron-ion plasmas is also pointed out.