Effects of superthermal electron on the features of nonlinear acoustic waves in unmagnetized collisionless ion pair plasma with superthermal electrons have been examined. The system equations are reduced in the form of the nonlinear Schrodinger equation. The rogue wave characteristics dependences on the ionic density ratio (ν = n–0/n+0), ionic mass ratio (Q = m+/m−), and superthermality index (κ) are investigated. It is worth mentioning that the results present in this work could be applicable in the Earth's ionosphere plasmas.

The mathematical new plasma wave solutions are specified in the compose of trigonometric, rational, hyperbolic, periodic and explosive kinds that are realistic for Modified-Kadomtsev-Petviashvili (MKP) equation. Also, numeral studies for the acquired solutions have been reveals that periodic, shock and explosive new forms may applicable in D-F Earth's ionosphere plasma. The used method is influential and robust in comparison applications in plasma fluids. To depict the propagating soliton profiles in a plasma medium, it is needful to solve MKP equation at a critical mass ratio. The Riccati–Bernoulli sub-ODE technique has been utilized to introduce some new important and applicable solutions. The number of these MKP solutions give a leading deed in applied ion acoustics in ionosphere.

Langmuir waves propagate in fractal complex plasma with fractal characteristics, which may cause some plasma particles to be trapped or causes wave turbulences. This phenomenon appears in the form of fractional order equations. Using an effective unified solver, some new solitary profiles such as rational, trigonometrically and hyperbolical functions forms are discussed, using fractional derivatives in conformable sense. The fractional order modulates the solitary properties, such as amplitudes and widths. The proposition technique can be executed to study many applied science models.