- [1] M. A. Abdou, Exact periodic wave solutions to some nonlinear evolution equations, Int. J. Nonlinear Sci., 6 (2008), 145–153.
- [2] M. J. Ablowitz and P. A. Clarkson, Nonlinear Evolution Equations and Inverse Scattering, Solitons, Cambridge University Press, Cambridge, UK, 1991.
- [3] O. D. Adeyemo, C. M. Khalique, Y. S. Gasimov, and F. Villecco, Variational and non-variational approaches with Lie algebra of a generalized (3+1)-dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation in Engineering and Physics, Alex. Eng. J., 63 (2023), 17–43.
- [4] O. D. Adeyemo, L. Zhang, and C. M. Khalique, Bifurcation theory, Lie group-invariant solutions of subalgebras and conservation laws of a generalized (2+1)-dimensional BK equation Type II in plasma physics and fluid mechanics, Mathematics, 10 (2022), 2391.
- [5] O. D. Adeyemo, L. Zhang, and C. M. Khalique, Optimal solutions of Lie subalgebra, dynamical system, travelling wave solutions and conserved currents of (3+1)-dimensional generalized ZakharovKuznetsov equation type I, Eur. Phys. J. Plus, 137 (2022), 954.
- [6] O. D. Adeyemo and C. M. Khalique, An optimal system of Lie subalgebras and group-invariant solutions with conserved currents of a (3+1)-D fifth-order nonlinear model with applications in electrical electronics, chemical engineering and pharmacy, J. Nonlinear Math. Phys., 30 (2023), 843–916.
- [7] O. D. Adeyemo, T. Motsepa, and C. M. Khalique, A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences, Alex. Eng. J., 61 (2022), 185–194.
- [8] O. D. Adeyemo, Applications of cnoidal and snoidal wave solutions via an optimal system of subalgebras for a generalized extended (2+1)-D quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering, J. Ocean Eng. Sci., 9 (2024), 126–153.
- [9] A. S. Alhasanat, On the minimal speed determinacy of traveling waves to a three-species competition model, Adv. Math. Models Appl., 8 (2023), 34–44.
- [10] U. Al Khawajaa, H. Eleuchb, and H. Bahloulid, Analytical analysis of soliton propagation in microcavity wires, Results Phys., 12 (2019), 471–474.
- [11] B. Babajanov and F. Abdikarimov, Expansion method for the loaded modified Zakharov-Kuznetsov equation, Adv. Math. Models Appl., 7 (2022), 168–177.
- [12] Y. Chen and Z Yan, New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method, Chaos Solitons Fract., 26 (2005), 399–406.
- [13] S. S. Chen, B. Tian, J. Chai, X. Y. Wu, and Z. Du, Lax pair, Lax pair binary Darboux transformations and dark-soliton interaction of a fifth-order defocusing nonlinear Schr¨odinger equation for the attosecond pulses in the optical fiber communication, Wave Random Complex, 30 (2020), 389–402.
- [14] C. Chun and R. Sakthivel, Homotopy perturbation technique for solving two point boundary value problemscomparison with other methods, Comput. Phys. Commun., 181 (2010), 1021–1024.
- [15] M. T. Darvishi and M. Najafi, A modification of extended homoclinic test approach to solve the (3+1)-dimensional potential-YTSF equation, Chin. Phys. Lett., 28 (2011), 040202.
- [16] S.T. Demiray and S. Duman, MTEM to the (2+1)-dimensional ZK equation and Chafee-Infante equation, Adv. Math. Models Appl., 6 (2021), 63–70.
- [17] X. X. Du, B. Tian, Q. X. Qu, Y. Q. Yuan, and X. H. Zhao, Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma, Chaos Solitons Fract., 134 (2020), 109709.
- [18] A.S. Farajov, On a solvability of the nonlinear inverse boundary value problem for the Boussinesq equation, Adv. Math. Models Appl., 7 (2022), 241–248.
- [19] X. Y. Gao, Y. J. Guo, and W. R. Shan, Shallow water in an open sea or a wide channel: Auto- and non-autoB¨acklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system, Chaos Solit. Fractals, 138 (2020), 109950.
- [20] X. Y. Gao, Y. J. Guo, and W. R. Shan, Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto-and non-auto-Bcklund transformations, Appl. Math. Lett., 104 (2020), 106170.
- [21] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th Edition, Academic Press, New York, 2007.
- [22] C. H. Gu, Soliton Theory and Its Application, Zhejiang Science and Technology Press, Zhejiang, China, 1990.
- [23] J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fract., 30 (2006), 700–708.
- [24] M. F. Hoque, H. O. Roshid, and F. S. Alshammari, Higher-order rogue wave solutions of the Kadomtsev Petviashvili-Benjanim Bona Mahony (KP-BBM) model via the Hirota bilinear approach, Phys. Scr., 95 (2020), 115215.
- [25] R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, UK, 2004.
- [26] W. X. Ma, T. Huang, and Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application, Phys. Scr., 82 (2010), 065003.
- [27] C. M. Khalique and O. D. Adeyemo, A study of (3+1)-dimensional generalized Korteweg-de Vries-ZakharovKuznetsov equation via Lie symmetry approach, Results Phys., 18 (2020), 103197.
- [28] C. M. Khalique and O. D. Adeyemo, Closed-form solutions and conserved vectors of a generalized (3+1)dimensional breaking soliton equation of engineering and nonlinear science, Mathematics, 8 (2020), 1692.
- [29] N. A. Kudryashov and N. B. Loguinova, Extended simplest equation method for nonlinear differential equations, Appl. Math. Comput., 205 (2008), 396-402.
- [30] N. A. Kudryashov, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos Solitons Fract., 24 (2005), 1217–1231
- [31] S. Liu, Multiple rogue wave solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili BenjaminBona-Mahony equation, Chinese. J. Phys., 68 (2020), 961–970.
- [32] V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, New York, USA, 1991.
- [33] A. Mekki and M. M. Ali, Numerical simulation of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equations using finite difference method, Appl. Math. Comput., 219 (2013), 11214–11222.
- [34] I. E. Mhlanga and C. M. Khalique, A study of a generalized Benney–Luke equation with time-dependent coefficients, Nonlinear Dyn., 90 (2017), 1535–1544.
- [35] E. Noether, Invariante variations probleme, Nachr. d. K¨onig. Gesellsch. d. Wiss. zu G¨ottingen, Math-phys. Klasse, 2 (1918), 235–257.
- [36] P. J. Olver, Applications of Lie Groups to Differential Equations, second ed., Springer-Verlag, Berlin, Germany, 1993.
- [37] M. S. Osman, One-soliton shaping and inelastic collision between double solitons in the fifth-order variablecoefficient Sawada-Kotera equation, Nonlinear Dynam., 96 (2019), 1491–1496.
- [38] L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, USA, 1982.
- [39] A. H. Salas and C. A. Gomez, Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation, Math. Probl. Eng., 2010.
- [40] M. Song, C. X. Yang, B. and G. Zhang, Exact solitary wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation, Appl. Math. Comput., 217 (2010), 1334–1339.
- [41] S. Q. Tang, X. L. Huang, and W. T. Huang, Bifurcations of travelling wave solutions for the generalized KP-BBM equation, Appl. Math. Comput., 216 (2010), 2881–2890.
- [42] K. U. H. Tariq and A. R. Seadawy, Soliton solutions of (3+1)-dimensional Korteweg-de Vries Benjamin-BonaMahony, Kadomtsev-Petviashvili Benjamin-Bona-Mahony and modified Korteweg de Vries-Zakharov-Kuznetsov equations and their applications in water waves, J. King. Saud. Univ. Sci., 31 (2019), 8–13.
- [43] M. Wang, X. Li, and J. Zhang, The (G0/G)− expansion method and travelling wave solutions for linear evolution equations in mathematical physics, Phys. Lett. A, 24 (2005), 1257–1268.
- [44] A. M. Wazwaz, Exact soliton and kink solutions for new (3+1)-dimensional nonlinear modified equations of wave propagation, Open Eng., 7 (2017), 169–174.
- [45] A. M. Wazwaz, Exact solutions of compact and noncompact structures for the KP-BBM equation, Nonlinear. Dyn., 169 (2005), 700–712.
- [46] A. M. Wazwaz, Partial Differential Equations, CRC Press, Boca Raton, Florida, USA, 2002.
- [47] A. M. Wazwaz, The tanh and sine-cosine method for compact and noncompact solutions of nonlinear Klein Gordon equation, Appl. Math. Comput., 167 (2005) 1179–1195.
- [48] A. M. Wazwaz, The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations, Appl. Math. Comput., 169 (2005), 321–338.
- [49] A. M. Wazwaz, Traveling wave solution to (2+1)-dimensional nonlinear evolution equations, J. Nat. Sci. Math., 1 (2007), 1–13.
- [50] J. Weiss, M. Tabor, and G. Carnevale, The Painl´ev´e property and a partial differential equations with an essential singularity, Phys. Lett. A, 109 (1985), 205–208.
- [51] Y. Xie and L. Li. Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev-Petviashvili BenjaminBona-Mahony equation near the offshore structure, Math. Comput. Simul., 193 (2022), 19–31.
- [52] Y. Yin, B. Tian, X.Y. Wu, H.M. Yin, Ch. R. Zhang, Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation for an offshore structure, Mod. Phys. Lett. B., 32 (2018), 1850031.
- [53] X. Zeng and D. S. Wang, A generalized extended rational expansion method and its application to (1+1)dimensional dispersive long wave equation, Appl. Math. Comput., 212 (2009), 296–304.
- [54] L. Zhang and C. M. Khalique, Classification and bifurcation of a class of second-order ODEs and its application to nonlinear PDEs, Discrete Contin. Dyn. Syst. - S., 11 (2018), 777–790.
- [55] C. R. Zhang, B. Tian, Q. X. Qu, L. Liu, and H. Y. Tian, Vector bright solitons and their interactions of the couple FokasLenells system in a birefringent optical fiber, Z. Angew. Math. Phys., 71 (2020), 1–19.
- [56] Y. Zhou, M. Wang, and Y. Wang, Periodic wave solutions to a coupled KdV equations with variable coefficients, Phys. Lett. A, 308 (2003), 31–36.
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