Constructing the soliton wave structure and stability analysis to generalized Calogero–Bogoyavlenskii–Schiff equation using improved simple equation method

Mina M. Fahim; Hamdy M. Ahmed; K. A. Dib; M. Elsaid Ramadan; Islam Samir; Mina M. Fahim; Hamdy M. Ahmed; K. A. Dib; M. Elsaid Ramadan; Islam Samir

doi:10.3934/math.2025501

AIMS Mathematics

2025, Volume 10, Issue 5: 11052-11070. doi: 10.3934/math.2025501

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Constructing the soliton wave structure and stability analysis to generalized Calogero–Bogoyavlenskii–Schiff equation using improved simple equation method

1.
Basic Sciences Department, Faculty of Engineering, The British University in Egypt, El‐Sherouk City, Egypt
2.
Mathematics Department, Faculty of Science, Fayoum University, Fayoum, Egypt
3.
Physics and Engineering Mathematics Department, Higher Institute of Engineering, El-Shorouk Academy, El Shorouk city, Cairo, Egypt
4.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia
5.
Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University, Abbassia, Cairo, Egypt

Received: 04 March 2025 Revised: 23 April 2025 Accepted: 28 April 2025 Published: 15 May 2025
MSC : 35B35, 35C07, 35C08, 35C09

In this work, we investigated the (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation, which models long wave propagation in shallow water and plays a significant role in fluid mechanics and plasma physics. Using the improved simple equations method, we obtained various solutions, including dark, bright, and singular solitons, and combinations of singular periodic solutions and exponential rational solutions. Additionally, we performed a linear stability analysis to examine the stability properties of these wave solutions. To further illustrate their characteristics during propagation, we provided 3D and contour plots for some opted wave solutions.
Citation: Mina M. Fahim, Hamdy M. Ahmed, K. A. Dib, M. Elsaid Ramadan, Islam Samir. Constructing the soliton wave structure and stability analysis to generalized Calogero–Bogoyavlenskii–Schiff equation using improved simple equation method[J]. AIMS Mathematics, 2025, 10(5): 11052-11070. doi: 10.3934/math.2025501

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Abstract

In this work, we investigated the (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation, which models long wave propagation in shallow water and plays a significant role in fluid mechanics and plasma physics. Using the improved simple equations method, we obtained various solutions, including dark, bright, and singular solitons, and combinations of singular periodic solutions and exponential rational solutions. Additionally, we performed a linear stability analysis to examine the stability properties of these wave solutions. To further illustrate their characteristics during propagation, we provided 3D and contour plots for some opted wave solutions.

References

[1]	G. Deng, Y. Gao, C. Ding, J. Su, Solitons and breather waves for the generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics, ocean dynamics and plasma physics, Chaos Soliton. Fract., 140 (2020), 110085. https://doi.org/10.1016/j.chaos.2020.110085 doi: 10.1016/j.chaos.2020.110085
[2]	S. Kumar, B. Mohan, R. Kumar, Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics, Nonlinear Dyn., 110 (2022), 693–704. https://doi.org/10.1007/s11071-022-07647-5 doi: 10.1007/s11071-022-07647-5
[3]	S. A. AlQahtani, M. E. M. Alngar, R. M. A. Shohib, A. M. Alawwad, Enhancing the performance and efficiency of optical communications through soliton solutions in birefringent fibers, J. Opt., 53 (2024), 3581–3591. https://doi.org/10.1007/s12596-023-01490-6 doi: 10.1007/s12596-023-01490-6
[4]	J. Yue, Z. Zhao, A. Wazwaz, Solitons, nonlinear wave transitions and characteristics of quasi-periodic waves for a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation in fluid mechanics and plasma physics, Chinese J. Phys., 89 (2024), 896–929. https://doi.org/10.1016/j.cjph.2024.03.039 doi: 10.1016/j.cjph.2024.03.039
[5]	J. Schiff, Integrability of Chern-Simons-Higgs vortex equations and a reduction of the Self-Dual Yang-Mills equations to three dimensions, In: Painlevé Transcendents, Boston, MA: Springer, 1992. https://doi.org/10.1007/978-1-4899-1158-2_26
[6]	Y. Li, H. An, Y. Zhang, Abundant fission and fusion solutions in the (2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation, Nonlinear Dyn., 108 (2022), 2489–2503. https://doi.org/10.1007/s11071-022-07306-9 doi: 10.1007/s11071-022-07306-9
[7]	Z. Zhao, L. He, $M$-lump and hybrid solutions of a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation, Appl. Math. Lett., 111 (2021), 106612. https://doi.org/10.1016/j.aml.2020.106612 doi: 10.1016/j.aml.2020.106612
[8]	H. Sheng, G. Yu, Y. Zhong, A special two-dimensional lattice by Blaszak and Szum: Solitons, breathers, lump solutions, and their interactions and dynamics, J. Math. Anal. Appl., 526 (2023), 127248. 10.1016/j.jmaa.2023.127248 doi: 10.1016/j.jmaa.2023.127248
[9]	X. Lü, S. Chen, Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types, Nonlinear Dyn., 103 (2021), 947–977. https://doi.org/10.1007/s11071-020-06068-6 doi: 10.1007/s11071-020-06068-6
[10]	L. Xu, X. Yin, N. Cao, S. Bai, Multi-soliton solutions of a variable coefficient Schrödinger equation derived from vorticity equation, nonlinear dynamics, Nonlinear Dyn., 112 (2024), 2197–2208. https://doi.org/10.1007/s11071-023-09158-3 doi: 10.1007/s11071-023-09158-3
[11]	T. Yin, Z. Xing, J. Pang, Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation, Nonlinear Dyn., 111 (2023), 9741–9752. https://doi.org/10.1007/s11071-023-08356-3 doi: 10.1007/s11071-023-08356-3
[12]	L. Li, C. Duan, F. Yu, An improved Hirota bilinear method and new application for a nonlocal integrable complex modified Korteweg-de Vries (MKdV) equation, Phys. Lett. A, 383 (2019), 1578–1582. https://doi.org/10.1016/j.physleta.2019.02.031 doi: 10.1016/j.physleta.2019.02.031
[13]	R. Zhang, S. Bilige, Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation, Nonlinear Dyn., 95 (2019), 3041–3048. https://doi.org/10.1007/s11071-018-04739-z doi: 10.1007/s11071-018-04739-z
[14]	P. Kumari, R. K. Gupta, S. Kumar, Non-auto-Bäcklund transformation and novel abundant explicit exact solutions of the variable coefficients Burger equation, Chaos Soliton. Fract., 145 (2021), 110775. https://doi.org/10.1016/j.chaos.2021.110775 doi: 10.1016/j.chaos.2021.110775
[15]	Z. Zhao, Bäcklund transformations, nonlocal symmetry and exact solutions of a generalized (2+1)-dimensional Korteweg–de Vries equation, Chinese J. Phys., 73 (2021), 695–705. https://doi.org/10.1016/j.cjph.2021.07.026 doi: 10.1016/j.cjph.2021.07.026
[16]	Z. Lan, $N$-soliton solutions, Bäcklund transformation and Lax Pair for a generalized variable-coefficient cylindrical Kadomtsev–Petviashvili equation, Appl. Math. Lett., 158 (2024), 109239. https://doi.org/10.1016/j.aml.2024.109239 doi: 10.1016/j.aml.2024.109239
[17]	Y. Li, B. Hu, L. Zhang, J. Li, The exact solutions for the nonlocal Kundu-NLS equation by the inverse scattering transform, Chaos Soliton. Fract., 180 (2024), 114603. https://doi.org/10.1016/j.chaos.2024.114603 doi: 10.1016/j.chaos.2024.114603
[18]	F. Yu, L. Li, Soliton robustness, interaction and stability for a variable coefficients Schrödinger (VCNLS) equation with inverse scattering transformation, Chaos Soliton. Fract., 185 (2024), 115185. https://doi.org/10.1016/j.chaos.2024.115185 doi: 10.1016/j.chaos.2024.115185
[19]	I. Samir, H. M. Ahmed, A. Darwish, H. H. Hussein, Dynamical behaviors of solitons for NLSE with Kudryashov's sextic power-law of nonlinear refractive index using improved modified extended tanh-function method, Ain Shams Eng. J., 15 (2024), 102267. https://doi.org/10.1016/j.asej.2023.102267 doi: 10.1016/j.asej.2023.102267
[20]	O. El-shamy, R. El-barkoki, H. M. Ahmed, W. Abbas, I. Samir, Exploration of new solitons in optical medium with higher-order dispersive and nonlinear effects via improved modified extended tanh function method, Alex. Eng. J., 68 (2023), 611–618. https://doi.org/10.1016/j.aej.2023.01.053 doi: 10.1016/j.aej.2023.01.053
[21]	W. B. Rabie, H. M. Ahmed, Optical solitons for multiple-core couplers with polynomial law of nonlinearity using the modified extended direct algebraic method, Optik, 258 (2022), 168848. https://doi.org/10.1016/j.ijleo.2022.168848 doi: 10.1016/j.ijleo.2022.168848
[22]	F. Ashraf, R. Ashraf, A. Akgül, Traveling waves solutions of Hirota–Ramani equation by modified extended direct algebraic method and new extended direct algebraic method, Int. J. Mod. Phys. B, 38 (2024), 2450329.
[23]	I. Samir, N. Badra, H. M. Ahmed, A. H. Arnous, Solitary wave solutions for generalized Boiti–Leon–Manna–Pempinelli equation by using improved simple equation method, Int. J. Appl. Comput. Math., 8 (2022), 102. https://doi.org/10.1007/s40819-022-01308-2 doi: 10.1007/s40819-022-01308-2
[24]	A. Bekir, A. C. Cevikel, The tanh–coth method combined with the Riccati equation for solving nonlinear coupled equation in mathematical physics, J. King Saud Univ.-Sci., 23 (2011), 127–132. https://doi.org/10.1016/j.jksus.2010.06.020 doi: 10.1016/j.jksus.2010.06.020
[25]	H. Chen, H. Zhang, New multiple soliton solutions to the general Burgers–Fisher equation and the Kuramoto–Sivashinsky equation, Chaos Soliton. Fract., 19 (2004), 71–76. https://doi.org/10.1016/S0960-0779(03)00081-X doi: 10.1016/S0960-0779(03)00081-X
[26]	X. Fu-Ding, C. Jing, L. Zhuo-Sheng, Using symbolic computation to exactly solve the integrable Broer–Kaup equations in (2+1)-dimensional spaces, Commun. Theor. Phys., 43 (2005), 585. https://doi.org/10.1088/0253-6102/43/4/003 doi: 10.1088/0253-6102/43/4/003
[27]	J. Manafian, O. A. Ilhan, H. F. Ismael, S. A. Mohammed, S. Mazanova, Periodic wave solutions and stability analysis for the (3+1)-D potential-YTSF equation arising in fluid mechanics, Int. J. Comput. Math., 98 (2021), 1594–1616. https://doi.org/10.1080/00207160.2020.1836358 doi: 10.1080/00207160.2020.1836358
[28]	Y. Zhao, T. Mathanaranjan, H. Rezazadeh, L. Akinyemi, M. Inc, New solitary wave solutions and stability analysis for the generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles, Results Phys., 43 (2022), 106083. https://doi.org/10.1016/j.rinp.2022.106083 doi: 10.1016/j.rinp.2022.106083
[29]	J. Manafian, O. A. Ilhan, A. Alizadeh, Periodic wave solutions and stability analysis for the KP-BBM equation with abundant novel interaction solutions, Phys. Scripta, 95 (2020), 065203. http://doi.org/10.1088/1402-4896/ab68be doi: 10.1088/1402-4896/ab68be

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