The head-on collision of ion acoustic solitary waves in a three-component unmagnetized plasma with cold ions, Boltzmann distributed positrons, and superthermal electrons is investigated using the extended Poincaré–Lighthill–Kuo method. The effects of the ratio of electron temperature to positron temperature, the spectral index, κ, of the electron kappa distribution, and fractional concentration of positron component (p) on the phase shift are studied. It is found that the presence of superthermal electrons play a significant role on the collision of ion acoustic solitary waves.

The properties of cylindrical and spherical dust acoustic (DA) solitary and shock waves in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Korteweg-de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of ion nonextensivity and dust kinematic viscosity on the basic features of DA solitary and shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar DA waves behave quite differently from their one-dimensional planar counterpart.

The nonlinear positron acoustic shock waves (PASWs) in an unmagnetized plasma consisting of cold positrons, immobile positive ions and Boltzmann-distributed electrons and hot positrons are studied in both unbounded planar geometry and bounded nonplanar geometry. In this regard, with the help of the reductive perturbation method, the cylindrical and spherical Korteweg–de Vries Burger (KdVB) equations are derived for PASWs. Numerically, the effects of several parameters and ion kinematic viscosities on the properties of PASWs in both planar and nonplanar geometry are discussed. It is found that PASWs in nonplanar geometry significantly differ from those in planar geometry.

The effects of unbounded planar geometry and bounded nonplanar geometry on quantum ion acoustic shock waves (QIASWs) in unmagnetized plasmas, where plasma kinematic viscosities are taken into account, are investigated. By the reductive perturbation method, deformed Korteweg–de Vries Burger (dKdVB), cylindrical, and spherical dKdVB equations are obtained for quantum ion acoustic shock waves in an unmagnetized two-species quantum plasma system, comprising electrons and ions. The properties of quantum ion acoustic shock waves are studied taking into account the quantum-mechanical effects in planar and nonplanar geometry. It is shown that quantum ion acoustic shock waves in nonplanar geometry differ from planar geometry. We have studied the change of QIASW structure due to the effect of the geometry, quantum parameter H, and ion kinematic viscosities by numerical calculations of the planar dKdVB, cylindrical, and spherical dKdVB equations.

Cylindrical and spherical modified Korteweg–de Vries (KdV) equations are derived for dust ion acoustic waves. It is shown that a suitable coordinate transformation reduces the cylindrical KdV equation into the ordinary KdV equation which can be solved analytically. A completely different analytical solution is obtained using the group analysis method. However, for cylindrical and spherical modified KdV equations group analysis method yields trivial analytical solutions. Numerically, solutions to these modified KdV equations are obtained assuming initial profiles similar to those in one-dimensional soliton solutions.