A new extended (2+1)-dimensional Kadomtsev–Petviashvili equation with N-solitons, periodic solutions, rogue waves, breathers and lump waves

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

“…Here, the Painlevé approach described 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); Wazwaz (2020, 2021, 2022a, 2022b); and in other references will be used to confirm the Painlevé integrability of equation (4). The solution to equation (4) is taken to be a Laurent expansion about a single manifold ψ ≡ ψ (x, y, z, t) as: …”

“…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.…”