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Research Article

Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method

, , , , , , & ORCID Icon show all
Pages 121-131 | Received 28 Oct 2023, Accepted 29 Jan 2024, Published online: 06 Feb 2024

References

  • Abazari, R., & Abazari, R. (2011). Hyperbolic, trigonometric and rational function solutions of Hirota-Ramani equation via G '/G -expansion method. Mathematical Problems in Engineering, 2011, 424801.
  • Abdel-Gawad, H. I., & Osman, M. (2014). Exact solutions of the Korteweg-de Vries equation with space and time dependent coefficients by the extended unified method. Indian Journal of Pure and Applied Mathematics, 45(1), 1–12. doi:10.1007/s13226-014-0047-x
  • Abdel-Gawad, H. I., & Osman, M. S. (2013). On the variational approach for analyzing the stability of solutions of evolution equations. Kyungpook Mathematical Journal, 53(4), 661–680. doi:10.5666/KMJ.2013.53.4.680
  • Abdou, M. A. (2007). The extended tanh method and its applications for solving nonlinear physical models. Journal of Applied Mathematics and Computing, 190(1), 988–996. doi:10.1016/j.amc.2007.01.070
  • Baskonus, H. M., Osman, M. S., Rehman, H. U., Ramzan, M., Tahir, M., & Ashraf, S. (2021). On pulse propagation of soliton wave solutions related to the perturbed Chen–Lee–Liu equation in an optical fiber. Optical and Quantum Electronics, 53(10), 556. doi:10.1007/s11082-021-03190-6
  • Bekir, A. (2009). The exp-function for Ostrovsky equation. The International Journal of Nonlinear Sciences and Numerical Simulation, 10, 735–739.
  • Boakye, G., Hosseini, K., Hinçal, E., Sirisubtawee, S., & Osman, M. S. (2024). Some models of Solitary wave propagation in optical fibers involving Kerr and parabolic laws. Optical and Quantum Electronics, 56(3), 345. doi:10.1007/s11082-023-05903-5
  • Borhanifar, A., & Moghanlu, A. Z. (2011). Application of the G’/G-expansion method for the Zhiber-Sabat equation and other related equations. Mathematical and Computer Modeling, 54(9-10), 2109–2116. doi:10.1016/j.mcm.2011.05.020
  • Chen, Y., & Wang, Q. (2005). Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1 + 1)-dimensional dispersive long wave equation. Chaos, Solitons & Fractals, 24(3), 745–757. doi:10.1016/j.chaos.2004.09.014
  • Demiray, S., Ünsal, Ö., & Bekir, A. (2014). New exact solutions for Boussinesq type equations by using (G'/G, 1/G) and (1/G')-expansion methods. Acta Physica Polonica A, 125(5), 1093–1098. doi:10.12693/APhysPolA.125.1093
  • Demiray, S., Ünsal, Ö., & Bekir, A. (2015). Exact solutions of nonlinear wave equations using (G′/G,1/G)-expansion method. Journal of the Egyptian Mathematical Society, 23(1), 78–84. doi:10.1016/j.joems.2014.02.011
  • Dusunceli, F. (2019). New exact solutions for generalized (3 + 1) Shallow Water-Like (SWL) equation. Applied Mathematics and Nonlinear Sciences, 4(2), 365–370. doi:10.2478/AMNS.2019.2.00031
  • Elagan, S. K., Sayed, M., & Hamed, Y. S. (2011). An innovative solutions for the generalized FitzHugh-Nagumo equation by using the generalized G’/G-expansion method. Applied Mathematics, 02(04), 470–474. doi:10.4236/am.2011.24060
  • El-Sherif, A. A., & Shoukry, M. M. (2007). Coordination properties of tridentate (N, O, O) heterocyclic alcohol (PDC) with Cu (II): Mixed ligand complex formation reactions of Cu (II) with PDC and some bio-relevant ligands. Spectrochimica acta. Part A, Molecular and Biomolecular Spectroscopy, 66(3), 691–700. doi:10.1016/j.saa.2006.04.013
  • Fahim, M. R. A., Kundu, P. R., Islam, M. E., Akbar, M. A., & Osman, M. S. (2022). Wave profile analysis of a couple of (3 + 1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach. Journal of Ocean Engineering and Science, 7(3), 272–279. doi:10.1016/j.joes.2021.08.009
  • Fan, E. (2000). Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4–5), 212–218. doi:10.1016/S0375-9601(00)00725-8
  • Fang, J., Nadeem, M., Habib, M., Karim, S., & Wahash, H. A. (2022). A new iterative method for the approximate solution of klein-gordon and sine-gordon equations. Journal of Function Spaces, 2022, 5365810. doi:10.1155/2022/5365810
  • Feng, J., Li, W., & Wan, Q. (2011). Using G '/G-expansion method to seek traveling wave solution of Kolmo gorov-Petrovskii-Piskunov equation. Journal of Applied Mathematics and Computing, 217(12), 5860–5865. doi:10.1016/j.amc.2010.12.071
  • Fetoh, A., Asla, K. A., El-Sherif, A. A., El-Didamony, H., & El-Reash, G. M. (2019). Synthesis, structural characterization, thermogravimetric, molecular modelling and biological studies of Co (II) and Ni (II) Schiff bases complexes. Journal of Molecular Structure, 1178, 524–537. doi:10.1016/j.molstruc.2018.10.066
  • Ganie, A. H., Sadek, L. H., Tharwat, M. M., Iqbal, M. A., Miah, M. M., Rasid, M. M., … Osman, M. S. (2023). New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering. Partial Differential Equations in Applied Mathematics, 9, 100608. doi:10.1016/j.padiff.2023.100608
  • He, C. H., & Liu, C. (2023). Variational principle for singular waves. Chaos Soliton Fract, 172, 113566. doi:10.1016/j.chaos.2023.113566
  • He, J. H., He, C. H., Sedighi, H. M., El Dib, Y. O., Marinkovic, D., & Alsolami, A. A. (2023). Analytical methods for nonlinear oscillators and solitary waves. Frontiers in Physics, 11, 1309182. doi:10.3389/fphy.2023.1309182
  • He, J. H., Hou, W. F., He, C. H., Saeed, T., & Hayat, T. (2021). Variational approach to fractal solitary waves. Fractals, 29(07), 2150199. doi:10.1142/S0218348X21501991
  • He, J.-H., & Wu, X.-H. (2006). Exp-function method for nonlinear wave equations. Chaos Soliton. Fract, 30(3), 700–708. doi:10.1016/j.chaos.2006.03.020
  • He, K., Nadeem, M., Habib, S., Sedighi, H. M., & Huang, D. (2022). Analytical approach for the temperature distribution in the casting-mould heterogeneous system. International Journal of Numerical Methods for Heat & Fluid Flow, 32(3), 1168–1182. doi:10.1108/HFF-03-2021-0180
  • Islam, M. N., Al-Amin, M., Akbar, A., Wazwaz, A. M., & Osman, M. S. (2023). Assorted optical soliton solutions of the nonlinear fractional model in optical fibers possessing beta derivative. Physica Scripta, 99(1), 015227. doi:10.1088/1402-4896/ad1455
  • Jabbari, A., Kheiri, H., & Bekir, A. (2011). Exact solutions of the coupled Higgs equation and the Miccari system using He’s Semi-Inverse Method and G’/G -expansion method. Computers & Mathematics with Applications, 62(5), 2177–2186. doi:10.1016/j.camwa.2011.07.003
  • Khalid, A., Alsubaie, A. S. A., Inc, M., Rehan, A., Mahmoud, W., & Osman, M. S. (2022). Cubic splines solutions of the higher order boundary value problems arise in sandwich panel theory. Results in Physics, 39, 105726. doi:10.1016/j.rinp.2022.105726
  • Kumar, D., Park, C., Tamanna, N., Paul, G. C., & Osman, M. S. (2020). Dynamics of two-mode Sawada-Kotera equation: Mathematical and graphical analysis of its dual-wave solutions. Results in Physics, 19, 103581. doi:10.1016/j.rinp.2020.103581
  • Liu, S., Fu, Z., Liu, S., & Zhao, Q. (2001). Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A, 289(1–2), 69–74. doi:10.1016/S0375-9601(01)00580-1
  • Lü, D. (2005). Jacobi elliptic function solutions for two variant Boussinesq equations. Chaos, Solitons & Fractals, 24(5), 1373–1385. doi:10.1016/j.chaos.2004.09.085
  • Mamun, M., Shahadat, A., Akbar, M. A., & Wazwaz, A. M. (2017). Some applications of the (G′/G, 1/G)-expansion method to find new exact solutions of NLEEs. The European Physical Journal - Plus, 132, 252.
  • Martínez, Y., Aguilar, H. G., & Atangana, A. J. F. (2018). First integral method for non-linear differential equations with conformable derivative. Mathematical Modelling of Natural Phenomena, 13(1), 14. doi:10.1051/mmnp/2018012
  • Miah, M. M., Iqbal, M. A., & Osman, M. S. (2023). A Study on stochastic longitudinal wave equation in a magneto-electro-elastic annular bar to find the analytical solutions. Communications in Theoretical Physics, 75(8), 085008. doi:10.1088/1572-9494/ace155
  • Nadeem, M., & He, J. H. (2021). He–Laplace variational iteration method for solving the nonlinear equations arising in chemical kinetics and population dynamics. Journal of Mathematical Chemistry, 59(5), 1234–1245. doi:10.1007/s10910-021-01236-4
  • Naher, H., Abdullah, F. A., & Akbar, M. A. (2011). The (G’/G)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation. Math. Probl. Eng, 2011, 218216. doi:10.1155/2011/218216
  • Öziş, T., & Aslan, İ. (2010). Application of the G’/G -expansion method to Kawahara type equations using symbolic computation. Applied Mathematics and Computation, 216(8), 2360–2365. doi:10.1016/j.amc.2010.03.081
  • Radha, B. R., & Duraisamy, C. (2021). The homogeneous balance method and its applications for finding the exact solutions for nonlinear equations. Journal of Ambient Intelligence and Humanized Computing, 12(6), 6591–6597. doi:10.1007/s12652-020-02278-3
  • Rehman, H. U., Akber, R., Wazwaz, A. M., Alshehri, H. M., & Osman, M. S. (2023). Analysis of Brownian motion in stochastic Schrödinger wave equation using Sardar sub-equation method. Optik, 289, 171305. doi:10.1016/j.ijleo.2023.171305
  • Rogers, C., & Shadwick, W. F. (1982). Backlund transformations. New York, NY: Academic Press.
  • Sadat, R., Kassem, M., & Ma, W.-X. (2018). Abundant lump-type solutions and interaction solutions for a nonlinear (3 + 1) dimensional model. Advances in Mathematical Physics, 2018, 9178480.
  • Shakeel, M., & Mohyud-Din, S. T. (2014). Soliton solutions for the positive Gardner_KP equation by (G′/G, 1/G)-expansion method. Ain Shams Engineering Journal, 5(3), 951–958. doi:10.1016/j.asej.2014.03.004
  • Soliman, A. A., Amin, M. A., El-Sherif, A. A., Sahin, C., & Varlikli, C. (2017). Synthesis, characterization and molecular modeling of new ruthenium (II) complexes with nitrogen and nitrogen/oxygen donor ligands. Arabian Journal of Chemistry, 10(3), 389–397. doi:10.1016/j.arabjc.2015.04.001
  • Tang, Y.-N., Ma, W.-X., & Xu, W. (2012). Grammian and Pfaffian solutions as well as Pfaffianization for a (3 + 1)-dimensional generalized shallow water equation. Chinese Physics B, 21(7), 070212. doi:10.1088/1674-1056/21/7/070212
  • Tian, B., & Gao, Y.-T. (1996). Beyond travelling waves: A new algorithm for solving nonlinear evolution equations. Com-puter Physics Communicatio, 95(2–3), 139–142. doi:10.1016/0010-4655(96)00014-8
  • Wang, M., Li, X., & Zhang, J. (2008). The (G’/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 372(4), 417–423. doi:10.1016/j.physleta.2007.07.051
  • Wazwaz, A.-M. (2004). A sine-cosine method for handing nonlinear wave equations. Mathematical and Computer Modeling, 40(5–6), 499–508. doi:10.1016/j.mcm.2003.12.010
  • Yusufoglu, E. (2008). New solitary for the MBBM equations using Exp-function method. Physics Letters A, 372, 442–446.
  • Zayed, E. M. E. (2010). Travelling wave solutions for higher dimensional nonlinear evaluation equations using G’/G expansion method. J. Appl. Math. Informatics, 28(1–2), 383–395.
  • Zhang, Y., Dong, H., Zhang, X., & Yang, H. (2017). Rational solutions and lump solutions to the generalized (3 + 1)-dimensional Shallow Water-like equation. Computers & Mathematics With Applications, 73(2), 246–252. doi:10.1016/j.camwa.2016.11.009