The attributes of the dust-acoustic solitary and periodic structures in the Saturn's inner magnetosphere

Abstract

The nonlinear characteristics of dust-acoustic (DA) structures including the localized and periodic waves in a plasma having Maxwellian ions and superthermal two-temperature electrons are investigated. The wave equations including both Kadomtsev-Petviashvili (KP) and modified KP (mKP) equations are derved using the reductive perturbation technique (RPT). The quantitative and qualitative characteristics of both compressive and rarefactive structures are studied. Jacobi elliptic function expansion method (JEFEM) is employed for the purpose of quantitative analysis while the qualitative behavior is studied by dint of the dynamical system approach. The solutions to the mKP equation hold at a critical condition where the quadratic nonlinearity ceases to exist. It is noticed that the KP equation admits only rarefactive solitary waves (SWs) whereas the mKP equation admits both compressive and rarefactive SWs. It is found that the profile (amplitude and width) of both DA solitary and periodic structures are different at different radii of Saturn's inner magnetosphere. The effect of kappa spectral index is studied and it is found that when the population of energetic cold electrons is decreased, the solitary structure gets energized. Our study is applied to Saturn's inner magnetosphere where kappa distributed two-temperature electrons and dust grains with gegative charge are observed by various satellite missions.

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).…”

“…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). In this plasma model, it was found the KP equation supports the propagation of negative solitons only, whereas the mKP equation admits the propagation of both positive and negative solitons.…”

“…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.…”