Proliferation of soliton, explosive, shocklike, and periodic ion-acoustic waves in Titan's ionosphere

Abstract

We report on many electrostatic nonlinear structures, namely, soliton, explosive, shocklike, and periodic waves, which may exist due to the dynamics of different ion species in Titan's ionosphere. Using the latest available observations of Titan at an altitude of ≈ 1300 km, the main ion components are HCNH+, C2H5+, and C3H5+. The dynamics of these waves are described by the Korteweg–de Vries (KdV) equation. Using the G′/G–expansion method, we obtain a class of solutions that elucidate these nonlinear structures. As the wave amplitude increases, both the width and velocity of the wave deviate from the prediction of the KdV equation. To describe the waves of larger amplitude, the higher-order dispersion has to be taken into account. The G′/G–expansion method is used, for the first time, to solve the KdV equation with higher-order dispersion. We compare between both KdV and higher-order dispersive KdV solutions, i.e., soliton, explosive, shocklike, and periodic waves.