New Variety Class of Solitons Arising From the (3+1)-Dimensional Evolution Equation
DOI:
https://doi.org/10.14738/aivp.1306.19766Keywords:
The (3 1)-dimensional nonlinear evolution equation, generalized Kudryashov method, extended direct algebraic method, (G'/G)-expansion method, Soliton solutionsAbstract
Our current work aimed constructing new variety soliton solutions to the completely integrable evolution (3+1)-dimensional nonlinear equation. The suggested model has strong relation with many equations especially with the Korteweg–De Vries (KDV) equation; it describes the real features in several branches of science as physics, fluid, engineering and technology. These soliton solutions of this model will be constructed for the first time using three distinct methods. The three employed methods are the generalized Kudryashov method (GKM), the extended direct algebraic method (EDAM) and (G'/G)-expansion method. The soliton solutions we obtained are novel compared to those previously reported by other authors using different methods.
References
Geng X. (2003); Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations; J. Phys. A: Math. Gen. 36, 2289–2303
Geng X. and Ma, Y. (2007); N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation, Phys. Lett. A 369(4), 285– 289
Wazwaz A. M. (2009); A (3+1)-dimensional nonlinear evolution equation with multiple soliton solutions and multiple singular soliton solutions, Appl. Math. Comput. 215(4), 1548–1552
Zhaqilao (2013); Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation, Physics Letters A 37, 3021-3026
Wazwaz A. M., A. (2013); variety of distinct kinds of multiple soliton solutions for a (3+1)-dimensional nonlinear evolution equations, Mathematical Methods in Applied Sciences 36, 2013, 349–357
Wazwaz A. M., A. (2014); New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions; Cent. Eur. J. Eng.; 4(4); 352-356
Yang, J.Y., Ma, W.X. (2017); Abundant lump-type solutions of the jimbo-miwa equation in (3+1)-dimensions, Comput. Math. Appl. 73 (2); 220–225.
Zhang, J.B., Ma, W.X. (2017); Mixed lump-kink solutions to the bkp equation, Comput. Math. Appl. 74 (3); 591–596.
Zhao, H.Q., Ma, W.X. (2017); Mixed lump-kink solutions to the kp equation, Comput. Math. Appl. 74 (6); 1399–1405.
Zhang,Y., Liu, Y., Tang, X.(2018); M-lump solutions to a (3 + 1)-dimensional nonlinear evolution equation
Loubna Ouahid, Saud Owyed , M.A. Abdou , Nawal A. Alshehri , S.K. Elagan, 2021; New optical soliton solutions via generalized Kudryashov’s scheme for Ginzburg–Landau equation in fractal order; Alexandria Engineering Journal; 60 (6); pages 5495-5510.
Dipankar Kumar , Aly R. Seadawy, Atish Kumar Joardar, (2018); Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology; Chinese Journal of Physics; 56 (1) pages 75-85.
Zahran, E., Bekir, A. (2022), Enormous soliton solutions to a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, Chinese Journal of Physics 77 1236–1252
Zahran, E., Hijaz, A., Askar, S., Botmart, T., Shehata, M. (2022); Dark-soliton behaviors arising from a coupled nonlinear Schrödinger system, Results in Physics 36: 105459
Zahran, E., Bekir, A. (2023); New diverse soliton solutions for the coupled Konno-Oono equations; Optical and Quantum Electronics; 55:112
Zahran, E., Bekir, A. (2022); Unexpected configurations for the optical solitons propagation in lossy fiber system with dispersion terms effect; Wiley; Math Meth Appl Sci. 2022;1–15.; DOI: 10.1002/mma.8738
Zahran, E., Bekir, A., Ibrahim, R. New impressive analytical optical soliton solutions to the Schrödinger-Poisson dynamical system against its numerical solutions. Opt. Quant. Electron. 55, 212 (2023)
Bekir, A. Zahran, E., Shehata, M., Comparison between the new exact and numerical solutions of the Mikhailov-Novikov-Wang equation, Numerical Method of Partial Differential Equation, 40, e22775 (2024)
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Copyright (c) 2025 Emad H. M. Zahran, Ali Gökhan Ertaş
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