Effects of the non-extensive parameter on the propagation of ion acoustic waves in five-component cometary plasma system

Some important evolution nonlinear partial differential equations are derived using the reductive perturbation method for unmagnetized collisionless system of five component plasma. This plasma system is a multi-ion contains negatively and positively charged Oxygen ions (heavy ions), positive Hydrogen ions (lighter ions), hot electrons from solar origin and colder electrons from cometary origin. The positive Hydrogen ion and the two types of electrons obey $q$-non-extensive distributions. The derived equations have three types of ion acoustic waves, which are soliton waves, shock waves and kink waves. The effects of the non-extensive parameters for the hot electrons, the colder electrons and the Hydrogen ions on the propagation of the envelope waves are studied. The compressive and rarefactive shapes of the three envelope waves appear in this system for the first order of the power of the nonlinearity strength with different values of non-extensive parameters. For the second order, the strength of nonlinearity will increase and the compressive type of the envelope wave only appears.