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Analysis of dynamics of fusion solitons of the generalized (3 +1)−Kadomtsev–Petviashvili equation | ||
Journal of Mahani Mathematical Research | ||
دوره 13، شماره 2 - شماره پیاپی 27، آبان 2024، صفحه 505-533 اصل مقاله (13.64 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.22632.1547 | ||
نویسندگان | ||
Muhammad Abubakar Isah* ؛ Asif Yokus | ||
Department of Mathematics, Faculty of Science, Firat University, Elazig, Turkey | ||
چکیده | ||
The aim of this paper is to introduce a generalized $(3+1)$-Kadomtsev-Petviashvili equation which is used to describe waves in a ferromagnetic medium. The equation's bilinear form is created and the new homoclinic test approach based on the Hirota bilinear form is used to find numerous novel precise solutions. These accurate solutions, which are depicted in the contour, two-dimensional and three-dimensional graphs, show the evolution of periodic characteristics. The modulation instability is used to investigate the stability of the obtained solutions. Additionally, the development of the fusion soliton is examined, as well as the fusion phenomenon in the traveling wave solution is described in the physical discussion. For this evolution equation, the study indicates new mechanical structures and various characteristics. The derived results back up the model that was proposed. These discoveries open up a new avenue for us to investigate the concept further. | ||
کلیدواژهها | ||
The new homoclinic test approach؛ Stability analysis؛ Fusion soliton؛ Kink soliton؛ Hirota bilinear method | ||
مراجع | ||
[1] Akram, G., Sadaf, M., & Khan, M. A. U. (2022). Abundant optical solitons for Lakshmanan–Porsezian–Daniel model by the modified auxiliary equation method. Optik, 251, 168163.
[2] Aziz, K. H. A. N., Abbas, K. H. A. N., & Sinan, M. (2022). Ion temperature gradient modes driven soliton and shock by reduction perturbation method for electron-ion magneto-plasma. Mathematical Modelling and Numerical Simulation with Applications, 2(1), 1-12.
[3] Cui, P. (2021). Bilinear form and exact solutions for a new extended (2+ 1)-dimensional Boussinesq equation. Results in Physics, 22, 103919.
[4] Darwish, A., Ahmed, H. M., Ammar, M., Ali, M. H., & Arnous, A. H. (2022). General Solitons and other solutions for coupled system of nonlinear Schrödinger’s equation in magneto-optic waveguides with anti-cubic law nonlinearity by using improved modified extended tanh-function method. Optik, 251, 168369.
[5] Duran, S. (2021). Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics. International Journal of Modern Physics B, 35(09), 2150130.
[6] Duran, S., Yokuş, A., & Durur, H. (2021). Surface wave behavior and refraction simulation on the ocean for the fractional Ostrovsky–Benjamin–Bona–Mahony equation. Modern Physics Letters B, 35(31), 2150477.
[7] Eskandar, S., & Hoseini, S.M. (2017). Nearly solitons for a perturbed higher-order nonlinear Schrodinger equation. J. Mahani math. res. 6(1), pp.43-56.
[8] Ghanbari, B. (2021). Employing Hirota’s bilinear form to find novel lump waves solutions to an important nonlinear model in fluid mechanics. Results in Physics, 29, 104689.
[9] Griffiths, G. W. (2012). Hirota Direct Method. City University, London.
[10] Hajiaghasi, S., & Azami, S. (2023). Gradient Ricci Bourguignon solitons on perfect fluid space-times. Journal of Mahani Mathematical Research, 1-12.
[11] He, J., Xu, S., & Porsezian, K. (2012). N-order bright and dark rogue waves in a resonant erbium-doped fiber system. Physical Review E, 86(6), 066603.
[12] Hu, W. Q., Gao, Y. T., Jia, S. L., Huang, Q. M., & Lan, Z. Z. (2016). Periodic wave, breather wave and travelling wave solutions of a (2+ 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas. The European Physical Journal Plus, 131, 1-19.
[13] Isah, M. A. (2023). A novel technique to construct exact solutions for the Complex Ginzburg-Landau equation using quadratic-cubic nonlinearity law. Mathematics in Engineering, Science & Aerospace (MESA), 14(1).
[14] Isah, M. A., Isah, I., Hassan, T. L., & Usman, M. (2021). Some characterization of osculating curves according to darboux frame in three dimensional euclidean space. International Journal of Advanced Academic Research, 7(12), 47-56.
[15] Isah, M. A., & Kulahci, M. A. (2019). Involute Curves in 4-dimensional Galilean space G4. In Conference Proceedings of Science and Technology (Vol. 2, No. 2, pp. 134-141). Murat TOSUN.
[16] Isah, M. A., Yokus, A., & Kaya, D. (2024). Exploring the influence of layer and neuron configurations on Boussinesq equation solutions via a bilinear neural network framework. Nonlinear Dynamics, 1-17. https://doi.org/10.1007/s11071-024-09708-3
[17] Isah, M. A., Yokus, A., & Kaya, D. (2024). Bilinear neural network method for obtaining the exact analytical solutions to nonlinear evolution equations and its application to KdV equation. Khayyam Journal of Mathematics. Accepted paper.
[18] Isah, M. A., & Yokus, A. (2023). Optical solitons of the complex Ginzburg-Landau equation having dual power nonlinear form using φ6-model expansion approach. Mathematical Modelling and Numerical Simulation with Applications, 3(3), 188-215.
[19] Isah, M. A., & Yokus, A. (2022). Application of the newly φ6- model expansion approach to the nonlinear reaction-diffusion equation. Open Journal of Mathematical Sciences. 6, 269-280. doi:10.30538/oms2022.0192
[20] Isah, M. A., & Yokus, A. (2023). Rogue waves and stability analysis of the new (2+ 1)-KdV equation based on symbolic computation method via Hirota bilinear form. In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA) (pp. 1-6). IEEE.
[21] Isah, M. A., & Yokus, A. (2024). Nonlinear Dispersion Dynamics of Optical Solitons of Zoomeron Equation with New φ6-Model Expansion Approach. Journal of Vibration Testing and System Dynamics, 8(03), 285-307.
[22] Isah, I., Isah, M. A., Baba, M. U., Hassan, T. L., & Kabir, K. D. (2021). On integrability of silver Riemannian structure. International Journal of Advanced Academic Research, 7(12), 2488-9849.
[23] Izadi, M., Yadav, S. K., & Methi, G. (2024). Two efficient numerical techniques for solutions of fractional shallow water equation. Partial Differential Equations in Applied Mathematics, 9, 100619.
[24] Jin-Ping, Y. (2001). Fission and fusion of solitons for the (1+ 1)-dimensional Kupershmidt equation. Communications in Theoretical Physics, 35(4), 405.
[25] Kaya, D., Yokuş, A., & Demiroğlu, U. (2020). Comparison of exact and numerical solutions for the Sharma–Tasso–Olver equation. Numerical solutions of realistic nonlinear phenomena, 53-65.
[26] Li, L., & Xie, Y. (2021). Rogue wave solutions of the generalized (3+ 1)-dimensional Kadomtsev–Petviashvili equation. Chaos, Solitons & Fractals, 147, 110935.
[27] Liu, J. G., Tian, Y., & Zeng, Z. F. (2017). New exact periodic solitary-wave solutions for the new (3+ 1)-dimensional generalized Kadomtsev-Petviashvili equation in multitemperature electron plasmas. AIP Advances, 7(10).
[28] Ma, W. X., & Fan, E. (2011). Linear superposition principle applying to Hirota bilinear equations. Computers & Mathematics with Applications, 61(4), 950-959. [29] Ma, W. X., & Zhu, Z. (2012). Solving the (3+ 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm. Applied Mathematics and Computation, 218(24), 11871-11879. [30] Mohammad, A. A., & Can, M. (1996). Painlevé analysis and symmetries of the Hirota– Satsuma equation. Journal of Nonlinear Mathematical Physics, 3(1-2), 152-155. [31] Myint-U, T., & Debnath, L. (2007). Linear partial differential equations for scientists and engineers. Springer Science & Business Media. [32] Rosenau, P. (2005). Communications-WHAT IS... a Compacton?. Notices of the American Mathematical Society, 52(7), 738-739. [33] Rosenau, P. (1994). Nonlinear dispersion and compact structures. Physical Review Letters, 73(13), 1737. [34] Rosenau, P., & Hyman, J. M. (1993). Compactons: solitons with finite wavelength. Physical Review Letters, 70(5), 564. [35] Tarla, S., Ali, K. K., & Yusuf, A. (2023). Exploring new optical solutions for nonlinear Hamiltonian amplitude equation via two integration schemes. Physica Scripta, 98(9), 095218. [36] Tarla, S., Ali, K. K., Yilmazer, R., & Yusuf, A. (2022). New behavior of tsunami and tidal oscillations for Long-and short-wave interaction systems. Modern Physics Letters B, 36(23), 2250116. [37] Tarla, S., Ali, K. K., Yusuf, A., Yılmazer, R., & Alquran, M. (2022). New explicit wave profiles of kundu-mukherjee-naskar equation through jacobi elliptic function expansion method. [38] Wazwaz, A. M. (2008). Multiple-front solutions for the Burgers–Kadomtsev–Petviashvili equation. Applied mathematics and computation, 200(1), 437-443. [39] Wazwaz, A. M. (2012). Multiple-soliton solutions for a (3+ 1)-dimensional generalized KP equation. Communications in Nonlinear Science and Numerical Simulation, 17(2), 491-495. [40] Wang, X. B., Tian, S. F., Yan, H., & Zhang, T. T. (2017). On the solitary waves, breather waves and rogue waves to a generalized (3+ 1)-dimensional Kadomtsev–Petviashvili equation. Computers & Mathematics with Applications, 74(3), 556-563. [41] Wang, S. (2022). Novel multi-soliton solutions in (2+ 1)-dimensional PT-symmetric couplers with varying coefficients. Optik, 252, 168495. [42] Wang, S., Tang, X. Y., Lou, S& . Y. (2004). Soliton fission and fusion: Burgers equation and Sharma–Tasso–Olver equation. Chaos, Solitons & Fractals, 21(1), 231-239. [43] Weiss, J. (1985). Modified equations, rational solutions, and the Painlevé property for the Kadomtsev–Petviashvili and Hirota–Satsuma equations. Journal of mathematical physics, 26(9), 2174-2180. [44] Yan, Z., & Konotop, V. V. (2009). Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities. Physical Review E, 80(3), 036607. [45] Yang, Q., & Zhang, H. (2021). On the exact soliton solutions of fifth-order Korteweg-de Vries equation for surface gravity waves. Results in Physics, 26, 104424. [46] Yokuş, A. (2021). Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines. Modern Physics Letters B, 35(32), 2150484. [47] Yokuş, A., Durur, H., Abro, K. A., & Kaya, D. (2020). Role of Gilson–Pickering equation for the different types of soliton solutions: a nonlinear analysis. The European Physical Journal Plus, 135, 1-19. [48] Yokuş, A., Durur, H., Duran, S., & Islam, M. T. (2022). Ample felicitous wave structures for fractional foam drainage equation modeling for fluid-flow mechanism. Computational and Applied Mathematics, 41(4), 174. [49] Yokus, A., & Isah, M. A. (2023). Dynamical behaviors of different wave structures to the Korteweg–de Vries equation with the Hirota bilinear technique. Physica A: Statistical Mechanics and its Applications, 622, 128819. [50] Yokus, A., & Isah, M. A. (2023). Stability analysis and soliton solutions of the nonlinear evolution equation by homoclinic technique based on Hirota bilinear form. In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA) (pp. 1-6). IEEE. [51] Yokus, A., & Isah, M. A. (2022). Stability analysis and solutions of (2+ 1)-Kadomtsev– Petviashvili equation by homoclinic technique based on Hirota bilinear form. Nonlinear Dynamics, 109(4), 3029-3040. [52] Zheng-De, D., Mu-Rong, J., Qing-Yun, D., & Shao-Lin, L. (2006). Homoclinic bifurcation for Boussinesq equation with even constraint. Chinese Physics Letters, 23(5), 1065. [53] Zheng-De, D., Zhen-Jiang, L., & Dong-Long, L. (2008). Exact periodic solitary-wave solution for KdV equation. Chinese Physics Letters, 25(5), 1531. [54] Zhang, Y., & Ma, W. X. (2015). Rational solutions to a KdV-like equation. Applied Mathematics and Computation, 256, 252-256. | ||
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