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• [1] Jhangeer, A., Hussain, A., Tahir, S., Sharif, S.: Solitonic, super nonlinear, periodic, quasiperiodic, chaotic waves and conservation laws of modified Zakharov-Kuznetsov equation in transmission line. Commun. Nonlinear Sci. Numer. Simul. 86, (2020).
• [2] Khalfallah, M.: New Exact traveling wave solutions of the (2+1) dimensional Zakharov-Kuznetsov (ZK) equation. An. St. Univ. Ovidius Constanta. 15(2), 35–44 (2007).
• [3] Ali, M. N., Seadawy, A. R., Husnine, S. M.: Lie point symmetries, conservation laws and exact solutions of (1 + n)-dimensional modified Zakharov–Kuznetsov equation describing the waves in plasma physics. Pramana - J. Phys. 91(48), 1-9 (2018).
• [4] Batiha, K.: Approximate analytical solution for the Zakharov–Kuznetsov equations with fully nonlinear dispersion. Journal of Computational and Applied Mathematics. 216, 157-163 (2008).
• [5] Ablowitz, M. X., Clarkson, P. A.: Solitons, nonlinear evolution equations and inverse scattering transform. Cambridge: Cambridge University Press, (1990).
• [6] Vakhnenko, V. O., Parkes, E. J., Morrison, A. J.: A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos Solitons and Fractals. 17(4), 683-692 (2003).
• [7] Rogers, C., Shadwick, W. F.: Bäcklund Transformations and Their Applications, Mathematics in Science and Engineering. Academic Press, New York, NY, USA (1982).
• [8] Jawad, A. J. M., Petkovic, M. D., Biswas, A.: Modified simple equation method for nonlinear evolution equations. Applied Mathematics and Computation. 217, 869–877 (2010).
• [9] Wang, M. L., Zhou, Y. B., Li, Z. B.: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Physics Letters Section A. 216(1–5), 67–75 (1996).
• [10] Seadawy, A. R., El-Rashidy, K.: Travelling wave solutions for some coupled nonlinear evolution equations by using the direct algebraic method. Mathematical and Computer Modelling. 57, 1371–1379 (2013).
• [11] Khater, M. M. A.: A hybrid analytical and numerical analysis of ultra-short pulse phase shifts. Chaos, Solitons and Fractals. 169, 113232 (2023).
• [12] Hirota, R.: Exact solution of the korteweg-de vries equation for multiple collisions of solitons. Physical Review Letters. 27(18), 1192–1194 (1971).
• [13] Malfliet,W., Hereman,W.: The tanh method. I: Exact solutions of nonlinear evolution and wave equations. Physica Scripta. 54(6), 563-568 (1996).
• [14] Wazwaz, A. M.: The tanh method for travelling wave solutions of nonlinear equations. Applied Mathematics and Computation. 154(3), 713-723 (2004).
• [15] El-Wakil, S. S., Abdou, M. A.: New exact travelling wave solutions using modified extended tanh-function method. Chaos Solitons and Fractals. 31(4), 840-852 (2007).
• [16] Fan, E.: Extended tanh-function method and its applications to nonlinear equations. Physics Letters A. 277(4-5), 212-218 (2000).
• [17] Wazwaz, A. M.: The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Applied Mathematics and Computation. 187(2), 1131-1142 (2007).
• [18] Liu, S., Fu, Z., Liu, S., Zhao, Q.: Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A. 289(1-2), 69–74 (2001).
• [19] Al-Muhiameed, A. Z. I., Abdel-Salam, E. A. B.: Generalized Jacobi elliptic function solution to a class of nonlinear Schrödinger-type equations. Mathematical Problems in Engineering. 2011 11 pages (2011).
• [20] Gepreel K. A., Shehata, A. R.: Jacobi elliptic solutions for nonlinear differential difference equations in mathematical physics. Journal of Applied Mathematics. 2012 15 pages (2012).
• [21] Yan Z., Zhang, H.: New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Physics Letters A. 285(5-6), 355–362 (2001).
• [22] Wazwaz, A. M.: A sine–cosine method for handling nonlinear wave equations. Mathematical and Computer Modelling. 40(5-6), 499-508(2004).
• [23] Wang, M., Li, X.: Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos, Solitons and Fractals. 24(5), 1257–1268 (2005).
• [24] Abdou, M. A.: The extended F-expansion method and its application for a class of nonlinear evolution equations. Chaos, Solitons and Fractals. 31(1), 95–104 (2007).
• [25] Khater, M. M. A.: Nonlinear elastic circular rod with lateral inertia and finite radius: Dynamical attributive of longitudinal oscillation. International Journal of Modern Physics B. 37(6) 2350052 (2023).
• [26] Fan, E., Zhang, H.: A note on the homogeneous balance method. Physics Letters A. 246(5), 403-406 (1998).
• [27] He, J. H.,Wu, X. H.: Exp-function method for nonlinear wave equations. Chaos, Solitons and Fractals. 30(3), 700–708 (2006).
• [28] Naher, H., Abdullah, F. A., Akbar, M. A.: New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the exp-function method. Journal of Applied Mathematics. 2012 (2012)14 pages.
• [29] Mohyud-Din, S. T., Noor, M. A.: Exp-function method for traveling wave solutions of modified Zakharov-Kuznetsov equation. Journal of King Saud University. 22(4), 213–216(2010).
• [30] Esen, A., Yagmurlu, N. M., Tasbozan, O.: Double exp-function method for multisoliton solutions of the Tzitzeica-Dodd-Bullough equation, Acta Mathematicae Applicatae Sinica, English Series. 32(2), 461-468 (2016).
• [31] Salas, A. H., Gomez, C. A.: Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation. Mathematical Problems in Engineering. 2010 (2010) 14 pages.
• [32] Ugurlu, Y., Kaya, D., Inan, I. E.: Comparison of three semianalytical methods for solving (1 + 1)-dimensional dispersive long wave equations. Computers & Mathematics with Applications. 61(5), 1278–1290 (2011).
• [33] Dinarvand, S., Khosravi, S., Doosthoseini, A., Rashidi, M. M.: The homotopy analysis method for solving the Sawada-Kotera and Laxs fifth-order KdV equations. Advances in Theoretical and Applied Mechanics. 1, 327–335 (2008).
• [34] Esen, A., Tasbozan, O., Yagmurlu, N. M.: Approximate Analytical Solutions of the Fractional Sharma-Tasso-Olver Equation Using Homotopy Analysis Method and a Comparison with Other Methods, Cankaya University Journal of Science and Engineering. 9(2), 139-147 (2012).
• [35] Biazar, J., Badpeima, F., Azimi, F.: Application of the homotopy perturbation method to Zakharov-Kuznetsov equations. Computers Mathematics with Applications. 58, 2391–2394 (2009).
• [36] Zafar, A., Raheel, M., Jafar, N., Nisar, K. S.: Soliton solutions to the DNA Peyrard Bishop equation with beta-derivative via three distinctive approache. The European Physical Journal Plus. 135, (2020).
• [37] Ali, K. K., Wazwaz, A. M., Mehanna, M. S., Osman, M. S.: On short-range pulse propagation described by (2 +1)-dimensional Schrodinger’s hyperbolic equation in nonlinear optical fibers,. Physica Scripta. 95(7), 075203 (2020).
• [38] Wu, X., Rui, W., Hong, X.: Exact travelling wave solutions of explicit type, implicit type and parametric type for K(m,n)equation, Journal of Applied Mathematics. 2012, 23 pages (2012) .
• [39] Zhang, R.: Bifurcation analysis for a kind of nonlinear finance system with delayed feedback and its application to control of chaos. Journal of Applied Mathematics. 2012, 18 pages (2012) .
• [40] Tascan, F., Bekir, A., Koparan, M.: Travelling wave solutions of nonlinear evolution equations by using the first integral method. Communications in Nonlinear Science and Numerical Simulation. 14, 1810–1815 (2009).
• [41] Munro, S., Parkes, E. J.: The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions. Journal of Plasma Physics. 62, 305-317 (1999).
• [42] Munro, S., Parkes, E. J.: Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation. Journal of Plasma Physics. 64, 411-426 (2000).
• [43] Khater, M. M. A.: In solid physics equations, accurate and novel soliton wave structures for heating a single crystal of sodium fluoride.International Journal of Modern Physics B. 377 2350068 (2023).
• [44] Zakharov, V. E., Kuznetsov, E. A.: On three-dimensional solitons. Soviet Physics. 39, 285288 (1974).
• [45] Hesam, S., Nazemi, A., Haghbin, A.: Analytical solution for the Zakharov-Kuznetsov equations by differential transform method,. International Journal of Mathematical and Computational Sciences. 5(3), 496-501(2011).
• [46] Schamel, H.: A modified Korteweg–de Vries equation for ion acoustic waves due to resonant electrons. Journal of Plasma Physics. 9, 377–387 (1973).
• [47] Liu, Y., Teng, Q., Tai, W., Zhou, J., Wang, Z.: Symmetry reductions of the (3 + 1)-dimensional modified Zakharov–Kuznetsov equation. Advances in Difference Equations. 2019, 2-14 (2019).
• [48] Park, C., Khater, M. M. A., Abdel-Aty, A. H., Attia, R. A. M., Lu, D. M.: On new computational and numerical solutions of the modified Zakharov–Kuznetsov equation arising in electrical engineering. Alexandria Engineering Journal. 59, 1099–1105 (2020).
• [49] Peng, Y. Z.: Exact Travelling Wave Solutions for a Modified Zakharov-Kuznetsov Equation. Acta Physica Polonica A. 115(3), 609-612 (2009).
• [50] Natiq, H., Said, M. R. M., Ariffin, M. R. K., He, S., Rondoni, L., Banerjee, S.: Self-excited and hidden attractors in a novel chaotic system with complicated multistability. The European Physical Journal Plus. 133, 557 (2018).
• [51] He, S., Banerjee, S., Sun, K.: Complex dynamics and multiple coexisting attractors in a fractional-order microscopic chemical system,. The European Physical Journal Special Topics. 228, 195-207 (2019).
• [52] Arecchi, F. T., Meucci, R., Puccioni, G., Tredicce, J.: Experimental Evidence of Subharmonic Bifurcations, Multistability, and Turbulence in a Q-Switched Gas Laser. Physical Review Letters. 49, 1217 (1982).
• [53] Natiq, H., Banerjee, S., Misra, A. P., Said, M. R. M.: Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers. Chaos Solitons and Fractals. 122, 58-68 (2019).
• [54] Morfu, S., Nofiele, B., Marquie, P.: On the use of multistability for image processing. Physics Letters A. 367, 192-198 (2007).
• [55] Rahim, M. F. A., Natiq, H., Fataf, N. A. A., Banerjee, S.: Dynamics of a new hyperchaotic system and multistability. The European Physical Journal Plus. 134, 499 (2019).
• [56] Li, C., Sprott, J. C.: Multistability in the Lorenz System: A Broken Butterfly. International Journal of Bifurcation and Chaos. 24, 1450131 (2014).
• [57] Yong, J., Haida, W., Changxuan, Y.: Multistability Phenomena in Discharge Plasma. Chinese Physics Letters. 5, 201-204 (1988).
• [58] Hahn, S. J., Pae, K. H.: Competing multistability in a plasma diode. Physics of Plasmas. 10, 314 (2003).
• [59] Prasad, P. K., Gowrishankar, A., Saha, A., Banerjee, S.: Dynamical properties and fractal patterns of nonlinear waves in solar wind plasma. Physica Scripta. 6(95), (2020).
• [60] Abdikian, A., Tamang, J., Saha, A.: Electron-acoustic supernonlinear waves and their multistability in the framework of the nonlinear Schrödinger equation. Communication in Theoretical Physics. 72, 075502(2020).
• [61] Pradhan, B., Saha, A., Natiq, H., Banerjee, S.: Multistability and chaotic scenario in a quantum pair-ion plasma. Zeitschrift für Naturforschung A. 76(2), 109-119 (2020).
• [62] Saha, A., Pradhan, B., Banerjee, S.: Multistability and dynamical properties of ion-acoustic wave for the nonlinear Schrödinger equation in an electron–ion quantum plasma. Physica Scripta. 5(95), 055602(2020).
• [63] Kudryashov, N. A.: Highly dispersive solitary wave solutions of perturbed nonlinear Schrodinger equations. Applied Mathematics and Computation. 371, 124972 (2020).
• [64] Saha, A., Ali, K. K., Rezazadeh, H., Ghatani, Y.: Analytical optical pulses and bifurcation analysis for the traveling optical pulses of the hyperbolic nonlinear Schrödinger equation. Optical and Quantum Electronics. 53, 150 (2021).
• [65] Lakshmanan, M., Rajasekar, S.: Nonlinear Dynamics. Heidelberg, Springer-Verlag, (2003).
• [66] Saha, A.: Bifurcation of travelling wave solutions for the generalized KP-MEW equations. Communications in Nonlinear Science and Numerical Simulation. 17, 3539 (2012).
• [67] Karakoc, S.B.G., Saha, A., Sucu, D.: A novel implementation of Petrov-Galerkin method to shallow water solitary wave pattern and superperiodic traveling wave and its multistability: generalized Korteweg-de Vries equation. Chinese Journal of Physics. 68, 605-617(2020).
• [68] Saha, A.: Bifurcation, periodic and chaotic motions of the modified equal width burgers (MEW-Burgers) equation with external periodic perturbation. Nonlinear Dynamics. 87, 2193-2201(2017).
• [69] Saha, A., Banerjee, S.: Dynamical Systems and Nonlinear Waves in Plasmas. CRC Press-Boca Raton, (2021).
• [70] Guckenheimer, J., Holmes, P. J.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. New York, Springer-Verlag (1983).