Ion-acoustic Waves at the Night Side of Titan’s Ionosphere: Higher-Order Approximation

Nonlinear solitary waves are investigated for a plasma system at the night side of Titan's ionosphere. The plasma model consists of three positive ions, namely C2H5+, HCNH+, and C3H5+, as well as Maxwellian electrons. The basic set of fluid equations is reduced to a Korteweg de-Vries (KdV) equation and linear inhomogeneous higher order KdV (LIHO-KdV) equation. The solitary wave solutions of both equations are obtained using a renormalization method. The solitary waves' existence region and the wave profile are investigated, and their dependences on the plasma parameters at the night side of Titan's ionosphere are examined. The solitary waves' phase velocities are subsonic or supersonic, and the propagating pulses are usually positive. The effect of higher-order corrections on the perturbation theory is investigated. It is found that the higher-order contribution makes the amplitude slightly taller, which is suitable for describing the solitary waves when the amplitude augments.