An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation
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Qianqian Guo
Abstract
This paper is devoted to investigating new non-traveling wave solutions for the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. By using the generalized variable separation method and extended three-wave approach, the process of solving the (3 + 1)-dimensional potential-YTSF equation is simplified and the interactions of multiple waves are revealed. With the aid of Maple, we derive thirty-six types new exact explicit non-traveling wave solutions with a like-parabolic tail. The main characteristic of these solutions is that they contain three arbitrary functions, which greatly enrich the diversity of solutions. This characteristic shows the novelty of our work. In particular, selecting suitable arbitrary functions, we can obtain traveling solutions, such as kink-wave solutions, solitary-wave solutions, kinky breather-wave solutions, singular solutions and periodic solutions. Then, some dynamical phenomena are exhibited by 3D representation, providing the complicated structure of the non-traveling wave solutions for the (3 + 1) dimensional potential-YTSF equation and their physical interpretation. In addition, our findings improve and extend the existing literature on related topics.
Funding source: Natural Science Foundation of Guangzhou Municipality
Award Identifier / Grant number: 202201011341
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: These authors contributed equally to this work. The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Competing interests: The authors state no conflict of interest.
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Research funding: This work is supported by the Basic Research Project of Guangzhou Science and Technology Plan (NO. 202201011341).
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Data availability: Not applicable.
References
[1] S. J. Yu, K. Toda, N. Sasa, and T. Fukuyama, “N soliton solutions to the Bogoyavlenskii–Schiff equation and a quest for the soliton solution in (3+1) dimensions,” J. Phys. A: Math. Gen., vol. 31, pp. 3337–3347, 1998, https://doi.org/10.1088/0305-4470/31/14/018.Search in Google Scholar
[2] C. L. Bai, X. Q. Liu, and H. Zhao, “Bäcklund transformation and multiple soliton solutions for (3+1)-dimensional potential-YTSF equation,” Commun. Theor. Phys., vol. 42, pp. 827–830, 2004, https://doi.org/10.1088/0253-6102/42/6/827.Search in Google Scholar
[3] Z. D. Dai, J. Liu, and D. L. Li, “Applications of HTA and EHTA to YTSF equation,” Appl. Math. Comput., vol. 207, pp. 360–364, 2009, https://doi.org/10.1016/j.amc.2008.10.042.Search in Google Scholar
[4] X. P. Zeng, Z. D. Dai, and D. L. Li, “New periodic soltion solutions for the (3+1)-dimensional potential-YTSF equation,” Chaos, Solitons Fractals, vol. 42, pp. 657–661, 2009, https://doi.org/10.1016/j.chaos.2009.01.040.Search in Google Scholar
[5] Z. T. Li and Z. D. Dai, “Exact periodic cross-kink wave solutions and breather type of two-solitary wave solutions for the (3+1)-dimensional potential-YTSF equation,” Comput. Math. Appl., vol. 61, pp. 1939–1945, 2011, https://doi.org/10.1016/j.camwa.2010.07.055.Search in Google Scholar
[6] Y. J. Hu, H. L. Chen, and Z. D. Dai, “New kink multi-soliton solutions for the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation,” Appl. Math. Comput., vol. 234, pp. 548–556, 2014, https://doi.org/10.1016/j.amc.2014.02.044.Search in Google Scholar
[7] W. Tan and Z. D. Dai, “Dynamics of kinky wave for (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation,” Nonlinear Dyn., vol. 85, pp. 817–823, 2016, https://doi.org/10.1007/s11071-016-2725-1.Search in Google Scholar
[8] A. D. Wazwaz, “Multiple-soliton solutions for the Calogero–Bogoyavlenskii–Schiff, Jimbo–Miwa and YTSF equations,” Appl. Math. Comput., vol. 203, pp. 592–597, 2008, https://doi.org/10.1016/j.amc.2008.05.004.Search in Google Scholar
[9] H. Q. Sun and A. H. Chen, “Interactional solutions of a lump and a solitary wave for two higher-dimensional equations,” Nonlinear Dyn., vol. 94, pp. 1753–1762, 2018, https://doi.org/10.1007/s11071-018-4454-0.Search in Google Scholar
[10] M. Foroutan, J. Manafian, and A. Ranjbaran, “Lump solution and its interaction to (3+1)-D potential-YTSF equation,” Nonlinear Dyn., vol. 92, pp. 2077–2092, 2018, https://doi.org/10.1007/s11071-018-4182-5.Search in Google Scholar
[11] M. Younis, S. Ali, S. T. R. Rizvi, M. Tantawy, K. U. Tariqe, and A. Bekir, “Investigation of solitons and mixed lump wave solutions with (3+1)-dimensional potential-YTSF equation,” Commun. Nonlinear Sci. Numer. Simul., vol. 94, p. 105544, 2021, https://doi.org/10.1016/j.cnsns.2020.105544.Search in Google Scholar
[12] L. Song and H. Zhang, “A new variable coefficient Korteweg–de Vries equation-based sub-equation method and its application to the (3+1)-dimensional potential-YTSF equation,” Appl. Math. Comput., vol. 189, pp. 560–566, 2007, https://doi.org/10.1016/j.amc.2006.11.119.Search in Google Scholar
[13] M. Song and Y. L. Ge, “Application of the G′/G-expansion method to (3+1)-dimensional nonlinear evolution equations,” Comput. Math. Appl., vol. 60, pp. 1220–1227, 2010, https://doi.org/10.1016/j.camwa.2010.05.045.Search in Google Scholar
[14] M. T. Darvishi and M. Najafi, “A modification of extended homoclinic test approach to solve the (3+1)-dimensional potential-YTSF equation,” Chin. Phys. Lett., vol. 28, p. 040202, 2011, https://doi.org/10.1088/0256-307x/28/4/040202.Search in Google Scholar
[15] J. G. Liu and Z. F. Zeng, “Multiple soliton solutions, soliton-type solutions and rational solutions for tile (3+1)-dimensional potential-YTSF equation,” Indian J. Pure Appl. Math., vol. 45, pp. 989–1002, 2014, https://doi.org/10.1007/s13226-014-0100-9.Search in Google Scholar
[16] Md. Shafiqul Islam, K. Khan, and M. Ali Akbar, “Exact travelling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation through the improved F-expansion method with Riccati equation,” Int. J. Comput. Sci. Math., vol. 8, pp. 61–72, 2017, https://doi.org/10.1504/ijcsm.2017.083128.Search in Google Scholar
[17] J. Manafian, O. A. Ilhan, H. F. Ismael, S. A. Mohammed, and S. Mazanova, “Periodic wave solutions and stability analysis for the (3+1)-D potential-YTSF equation arising in fluid mechanics,” Int. J. Comput. Math., vol. 98, pp. 1594–1616, 2021, https://doi.org/10.1080/00207160.2020.1836358.Search in Google Scholar
[18] C. K. Kuo, Y. C. Chen, C. W. Wu, and W. N. Chao, “Novel solitary and resonant multi-soliton solutions to the (3+1)-dimensional potential-YTSF equation,” Mod. Phys. Lett. B, vol. 35, p. 2150326, 2021, https://doi.org/10.1142/s0217984921503267.Search in Google Scholar
[19] Z. Y. Yan, “New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation,” Phys. Lett. A, vol. 318, pp. 78–83, 2003, https://doi.org/10.1016/j.physleta.2003.08.073.Search in Google Scholar
[20] T. X. Zhang, H. N. Xuan, D. F. Zhang, and C. J. Wang, “Non-travelling wave solutions to a (3+1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures,” Chaos, Solitons Fractals, vol. 34, pp. 1006–1013, 2007, https://doi.org/10.1016/j.chaos.2006.04.005.Search in Google Scholar
[21] N. Yuan, “Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation,” Opt. Eng., vol. 57, p. 043107, 2018, https://doi.org/10.1117/1.oe.57.4.043107.Search in Google Scholar
[22] L. B. Lv and Y. D. Shang, “Abundant new non-travelling wave solutions for the (3+1)-dimensional potential-YTSF equation,” Appl. Math. Lett., vol. 107, p. 106456, 2020, https://doi.org/10.1016/j.aml.2020.106456.Search in Google Scholar
[23] Y. D. Shang, “Abundant explicit non-traveling wave solutions for the (2+1)-dimensional breaking soliton equation,” Appl. Math. Lett., vol. 131, p. 108029, 2022, https://doi.org/10.1016/j.aml.2022.108029.Search in Google Scholar
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- Complexiton and interaction solutions to a specific form of extended Calogero–Bogoyavlenskii–Schiff equation via its bilinear form
- An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation
- The Riemann Hilbert dressing method and wave breaking for two (2 + 1)-dimensional integrable equations
Articles in the same Issue
- Frontmatter
- Research Articles
- Analytical and numerical studies of a cancer invasion model with nonlocal diffusion
- Exploration of different multi-peak solitons and vibrant breather type waves’ solutions of nonlinear Schrödinger equations with advanced dispersion and cubic–quintic nonlinearity, unveiling their applications
- Leader-following consensus tracking control for fractional-order multi-motor systems via disturbance-observer
- A numerical approach for solving nonlinear fractional Klein–Gordon equation with applications in quantum mechanics
- On the construction of various soliton solutions of two space-time fractional nonlinear models
- RANS study of surface roughness effects on ship resistance
- Complexiton and interaction solutions to a specific form of extended Calogero–Bogoyavlenskii–Schiff equation via its bilinear form
- An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation
- The Riemann Hilbert dressing method and wave breaking for two (2 + 1)-dimensional integrable equations
