Zakharov–Kuznetsov (ZK) equation for ion-acoustic waves (IAWs) is derived using the reductive perturbation method (RPM) in magnetised plasma consisting of ions, positrons and nonthermal electrons in small but finite amplitude limit. Propagation characteristics of ion-acoustic solitary waves (IASWs) in three-dimensional space are analysed to determine their region of existence. Investigations reveal that ion-acoustic solitary pulses (IASPs) may exist in such plasmas and presence of nonthermal electrons significantly affects the amplitude and width of solitary pulses. Dependence of velocity, amplitude and width of solitary pulses on plasma parameters arepresented graphically. The amplitude of soliton increases with increase in ion temperature ratio ($\sigma$) and positron concentration ($\alpha$). However, it decreases with increase in nonthermal electron parameter ($\beta$) keeping other plasma parameters constant. Width of the soliton increases with increase in $\beta$, $\sigma$ and $\alpha$. Phase velocity of ion-acoustic wave ($\lambda$) increases with increase in nonthermal $\beta$ and $\sigma$. In our analysis, we found that magnetisation of plasma affect the width of the soliton but not the amplitude.

Ion-acoustic solitary waves (IASWs) in plasma consisting of ions, positrons and superthermal electrons in two distinct temperatures have been studied. The reductive perturbation method (RPM) has been employed to derive the Korteweg–de Vries and modified KdV equation. Numerical and analytical studies show that compressive and rarefactive solitons exist for the selected parametric range depending on the spectral indexes, $κ (κ_{h},κ_{c})$ and their respective densities ($\nu,\mu$). It is found that spectral indexes ($κ_{h},κ_{c}$) and their relative densities have significant impact on the basic properties, i.e., amplitude and width as well as on the nature of IASWs. Variations of amplitude and width for the compressive and rarefactive solitary waves have been analysed graphically with different plasma parameters like spectral indexes of cold and hot electrons ($k_{c}, k_{h}$), their respective densities, ionic temperature ratio, positron temperature ratio as well as with the temperature ratio of the two-electron species. The amplitude of the compressive (rarefactive) solitary waves increases (decreases) on increasing $k_{h}$. However, the amplitude of the compressive (rarefactive) solitary waves decreases (increases) on increasing $k_{c}$. The investigations of such solitary waves may be helpful for the critical understanding of space where superthermal electrons with two different temperatures exist along with positrons and ions (e.g. Saturn’s magnetosphere, pulsar magnetosphere).

Nonlinear propagation of an ion-acoustic dressed soliton is studied in unmagnetised plasma consisting of ion, positron and non-thermal electron. The exact soliton solution is derived using the reductive perturbation method (RPM) with the help of renormalisation procedure. This exact solution reduces to the dressed soliton solution when Mach number is expanded in terms of soliton velocity. The effects of non-thermal electrons, soliton velocity and Mach number on the characteristics (amplitude, width and product of amplitude and square of width) of the KdV soliton, core structure, dressed soliton and exact soliton are discussed in detail.