Formation and interaction of multi-dimensional electrostatic ion-acoustic solitons in two-electron temperature plasmas

Abstract

Ion-acoustic waves (IAWs) are investigated in an unmagnetized collisionless plasma comprising dynamical ions and inertialess cold and hot (C-H) electrons expressed by Maxwellian, kappa, and (r,q) distributions. The reductive perturbation theory is applied for deriving a modified Kadomtsev-Petviashvili (mKP) equation to examine the characteristics of ion-acoustic structures (solitary waves). The Hirota bilinear formalism is used to investigate the propagation of a single soliton and the interaction of two solitons with special reference to space plasmas. It is found that ratio of number density of cold to hot electrons and non-Maxwellian nature of cold electrons not only affect the propagation characteristics of single mKP solitons but also alter the interaction time of the IASWs. It is found that the swiftness of the interaction of solitons for flat-topped distribution surpasses both kappa and Maxwellian distributions. It is also found that the bipolar and tripolar structures depend on the ratio of the propagation vectors. The ranges of electric field amplitude for the IASWs are calculated for C-H electrons distributions corresponding to Saturn's B-ring and the region just beyond terrestrial magnetopause, and are shown to agree with Cassini Wideband Receiver (WBR) observational data and Wideband plasma wave instrument's waveform data.

An extended Painlevé integrable Kadomtsev--Petviashvili equation with lumps and multiple soliton solutions

“…The KP-type equation is a significant equation with numerous uses in a wide range of scientific fields such as a plasma and mechanical fluid. The KP-type equation explains the propagation of long waves of small amplitude in different plasma systems if the perturbations is considered in two-dimensional space (Feng and Zhang, 2019; Wazwaz, 2022a, 2022b; Ma et al , 2021a; Ma et al , 2021b; Adeyemo and Khalique, 2022; Lingfei et al , 2022; Wazwaz, 2011a; Wazwaz and El-Tantawy, 2017; Wazwaz, 2018; Kaur and Wazwaz, 2018; Ali et al , 2023; Shohaib, 2022a, 2022b). For instance, the dust-acoustic (DA) solitary waves (SWs) and periodic structures in a collisionless unmagnetized superthermal plasma have been investigated by analyzing both KP and modified KP (mKP) equations (Ali et al , 2023).…”

“…As proposed in the literature, the KP equation was extended in two ways: and that were thoroughly examined in (Ma et al , 2021a; Ma et al , 2021b; Adeyemo and Khalique, 2022; Lingfei et al , 2022; Wazwaz, 2011a; Wazwaz and El-Tantawy, 2017; Wazwaz, 2018; Kaur and Wazwaz, 2018; Ali et al , 2023; Shohaib, 2022a, 2022b), where λu tt and μu ty are included in the standard KP equation (1) to construct equation (2) and the linear terms α24utt,αuty, and βu xt were added to give the second KP equation (3). Note that the coefficients λ , β and μ do not equal to zero.…”

“…The additional term βu xt in equation (3) proved to retrieve the integrability of equation (2). More extensions of the KP equation can be found in the literature in Ma et al (2021a); Ma et al (2021b); Adeyemo and Khalique (2022), Lingfei et al (2022); Wazwaz (2011a); Wazwaz and El-Tantawy (2017), Wazwaz (2018); Kaur and Wazwaz (2018), Ali et al (2023); Shohaib (2022a, 2022b); and in some of the references therein. The aforementioned equations can simulate internal and surface waves in channels or straits.…”

“…Moreover, we shall demonstrate that the new additional terms do not affect the integrability property of the proposed KP equation. The MSSs will be formally derived using the efficient HBM (Ma et al , 2021a; Ma et al , 2021b; Adeyemo and Khalique, 2022; Lingfei et al , 2022; Wazwaz, 2011a; Wazwaz and El-Tantawy, 2017; Wazwaz, 2018; Kaur and Wazwaz, 2018; Ali et al , 2023; Shohaib, 2022a, 2022b). Furthermore, a class of localized LSs for this novel equation will be presented using different values of the used parameters.…”

“…For investigating the soliton interaction, Hirota bilinear method (HBM) was carried out for analyzing the mKP equation (Shohaib, 2022a). Moreover, the propagation of electrostatic ion-acoustic SWs in a collisionless plasma containing inertial positive ions and inertialess two temperature electrons have been examined by reducing the fluid model equations to the mKP equation (Shohaib, 2022b). The HBM was applied for solving the mKP equation and investigating the single soliton propagation as well as the two solitons interaction.…”