Abstract
This paper deals with the extraction of exact solutions of nonlinear extended quantum Zakharov–Kuznetsov equation by implementing well founded approaches like generalized exponential rational function method and \(\left( \frac{G^{\prime}}{G},\frac{1}{G}\right) \) expansion method. Singular, periodic, hyperbolic and rational function solutions are achieved for particular values of parameters. The obtained solutions are discussed graphically by plotting 2D line plots and 3D surface plots. This research findings demonstrate that applying these approaches is a feasible means of solving numerous precise PDE solutions. The computations are worked out in this script with the aid of Mathematica software.
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References
Ali, K.K., Yilmazer, R., Yokus, A., Bulut, H.: Analytical solution for the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznestov equation in plasma physics. Phys. A 548, 124327 (2020)
Aly, R.S., Lu, D.: Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma. Result Phys. 6, 590–593 (2016)
Areshi, M., Seadawy, A.R., Ali, A., Aljohani, A.F., Alharbi, W.: Construction of solitary wave solutions to the (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations arising in quantum plasma physics. Symmetry 15(248), 1491–1496 (2023)
Ebadi, G., Mojavir, A., Milovic, D., Johnson, S., Biswas, A.: Solitons and other solutions to the quantum Zakharov–Kuznetsov equation. Astro Phys. Space Sci. 341, 507–513 (2012)
Ghanbari, B., Baleanu, D.: New optical solutions of the fractional gerdjikov-ivanov equation with conformable derivative. Front. Phys. 8, 167 (2020). https://doi.org/10.3389/fphy.2020.00167
Ghanbari, B., Khater, M.A.M.: On the solitary wave solutions and physical characterization of gas diffusion in a homogeneous medium via some efficient techniques. Eur. Phys. J. Plus 136, 447 (2021). https://doi.org/10.1140/epjp/s13360-021-01457-1
Ghanbari, B.: Abundant soliton solutions for the Hirota Maccari equation via the generalized exponential rational function method. Mod. Phys. Lett. B 33(9), 1950106 (2019)
Ghanbari, B., Akgul, A.: Abundant new analytical and approximate solutions to the generalized Schamel equation. Front. Phys. (2020). https://doi.org/10.1088/1402-4896/ab8b27
Ghanbari, B., Gomez, A.J.F.: Optical soliton solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation. Mod. Phys. Lett. B 33(32), 1950402 (2019)
Ghanbari, B., Inc, M.M.: A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation. Eur. Phys. J. Plus 133, 142 (2018)
Ghanbari, B., Akgul, A., Osman, M.S.: Generalized exponential rational function method for extended Zakharov–Kuzetsov equation with conformable derivative. Mod. Phys. Lett. A 34(20), 1950155 (2019)
Khater, M.A.M.: Long waves with a small amplitude on the surface of the water behave dynamically in nonlinear lattices on a non-dimensional grid. Int. J. Mod. Phys. B 37(9), 2350188 (2023)
Khater, M.A.M.: Abundant and accurate computational wave structures of the nonlinear fractional biological population model. Int. J. Mod. Phys. B 37(18), 2350176 (2023a)
Khater, M.A.M.: Analyzing pulse behavior in optical fiber: Novel solitary wave solutions of the perturbed Chen–Lee–Liu equation. Int. J. Mod. Phys. B 37(34), 2350177 (2023b)
Khater, M.A.M.: Computational simulations of propagation of a tsunami wave across the ocean. Chaos Solitons Fractals 174, 113806 (2023c)
Khater, M.A.M.: Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers. Chaos Solitons Fractal 167(34), 113098 (2023d)
Khater, M.A.M.: A hybrid analytical and numerical analysis of ultra—short pulse phase shifts. Chaos Solitons Fractals 174, 113232 (2023e)
Khater, M.A.M.: Hybrid accurate simulations for constructing some novel analytical and numerical solutions of three-order GNLS equation. Int. J. Geom. Methods Mod. Phys. 20(9), 2350159 (2023f)
Kumar, S., Wazwaz, A.-M., Kumar, A.: New exact solitary wave solutions of the strain wave equation in microstructured solids via the generalized exponential rational function method. Eur. Phys. J. Plus 135, 1–17 (2020)
Moslem, W.M., Ali, S., Shukla, P.K., Tang, X.Y., Rowlands, G.: Solitary, explosive and periodic solutions of the quantum Zakharov–Kuznetsov equation and its transverse instability. Phys. Plasmas 14(8), 082308 (2007)
Sabry, R., Moslem, W.M., Haas, F., Shukla, P.K.: Explosive, soliton, and shock in a quantum electron-positron-ion magnetoplasma. Phys. Plasma 15, 122308 (2008)
Senol, M., Gencyigit, M., Qureshi, S.: New analytical and numerical solutions to the (2+1)-dimensional conformable cpKP - BKP equation arising in fluid dynamics, plasma physics, and nonlinear optics. Opt. Quantum Electron. 56, 352 (2024)
Wazwaz, A.M., Akbar, A., Alia, S.H.M.: Some applications of the \(({G^{\prime }/G}, {1/G})\)-expansion method to find new exact solutions of NLEEs. Eur. Phys. J. Plus (2017). https://doi.org/10.1140/epjp/i2017-11571-0
Yan, Z.: Periodic, solitary and rational wave solutions of the 3D extended quantum Zakharov Kuznetsov equation in dense quantum plasmas. Phys. Lett. A 373(18), 2432–2437 (2009)
Zakharov, V.E., Kuznetsov, E.A.: Three-dimensional solitons. Sov. Phys. 39(2), 285–286 (1974)
Zayed, E.M.E., Abdelaziz, M.A.M.: The two-variable \(({G^{\prime }/G}, {1/G})\)-expansion method for solving the nonlinear KdV - mKdV equation. Math. Probl. Eng. 14, 725061 (2012)
Zayed, E.M.E., Alurrfi, K.A.E.: Extended generalized Zakh G’/G -expansion method for solving the nonlinear quantum Zakharov–Kuznetsov equation. Ricerche di matematica 65, 235–254 (2016)
Zayed, E.M.E., Shohib, R.M.A., Al-Nowehy, A.G.: Solitons and other solutions for higher-order NLS equation and quantum Zakharov–Kuznestov equation using the extended simplest equation method. Comput. Math. Appl. 76, 2286–2303 (2018)
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Akram, G., Arshed, S., Sadaf, M. et al. Extraction of new soliton solutions of (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation via generalized exponential rational function method and \(\left( \frac{G^{\prime }}{G},\frac{1}{G}\right) \) expansion method. Opt Quant Electron 56, 829 (2024). https://doi.org/10.1007/s11082-024-06662-7
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DOI: https://doi.org/10.1007/s11082-024-06662-7