Painlevé analysis, Bäcklund transformations and traveling-wave solutions for a \((3 + 1)\)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid. (English) Zbl 1462.35338
Summary: Fluids are seen in such disciplines as atmospheric science, oceanography and astrophysics. In this paper, we investigate a \((3 + 1)\)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid. On the basis of the Painlevé analysis, we find that the equation is Painlevé integrable under a certain constraint. Through the truncated Painlevé expansion, we give an auto-Bäcklund transformation. By virtue of the Hirota method, we derive a bilinear auto-Bäcklund transformation. Via the polynomial-expansion method, traveling-wave solutions are obtained. We observe that the amplitude of a traveling wave remains invariant during the propagation. We graphically demonstrate that the amplitude of the traveling-wave is affected by the coefficients corresponding to the dispersion and nonlinearity effects, while other coefficients have no influence on the traveling-wave amplitude, which represent the perturbed effects and disturbed wave velocity effects.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C07 | Traveling wave solutions |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
Keywords:
fluid; \((3 + 1)\)-dimensional generalized Kadomtsev-Petviashvili equation; Painlevé analysis; Bäcklund transformations; traveling wavesReferences:
| [1] | O. A. Bég et al., Chin. J. Phys.60, 167 (2019); L. Hu et al., Z. Angew. Math. Phys.72, 75 (2021). |
| [2] | Romatschke, P., Phys. Rev. Lett.120, 012301 (2018). |
| [3] | Wang, C.et al., Appl. Energy120, 012301 (2018). |
| [4] | Elger, D. F.et al., Engineering Fluid Mechanics (John Wiley & Sons, Hoboken, 2020). |
| [5] | Fox, R. W., McDonald, A. T. and Mitchell, J. W., Fox and McDonalds Introduction to Fluid Mechanics (John Wiley & Sons, New York, 2020). |
| [6] | Y. J. Feng et al., Eur. Phys. J. Plus135, 272 (2020); T. T. Jia et al., Nonlinear Dyn. 98, 269 (2019). |
| [7] | Wu, H. Y. and Jiang, L. H., Nonlinear Dyn.97, 403 (2019). |
| [8] | Tamang, J. and Saha, A., Phys. Plasmas27, 012105 (2020). |
| [9] | Li, P., Malomed, B. A. and Mihalache, D., Opt. Exp.28, 34472 (2020). |
| [10] | Su, J. J.et al., Phys. Rev. E100, 042210 (2019). |
| [11] | Chen, J. H.et al., Phys. Rev. Lett.123, 173902 (2019). |
| [12] | Su, J. J., Gao, Y. T. and Ding, C. C., Appl. Math. Lett.88, 201 (2019). · Zbl 1448.76087 |
| [13] | Ding, C. C.et al., Chaos Solitons Fract.133, 109580 (2020). |
| [14] | Tian, S. F. and Ma, P. L., Commun. Theor. Phys.62, 245 (2014). · Zbl 1297.35210 |
| [15] | Li, M. Z.et al., Mod. Phys. Lett. B32, 1850223 (2018). |
| [16] | Wang, M.et al., Chin. J. Phys.60, 440 (2019). |
| [17] | Hu, C. C.et al., Comput. Math. Appl.78, 166 (2019). |
| [18] | Yu, W. T.et al., Nonlinear Dyn.100, 1611 (2020). |
| [19] | Hirota, R., The Direct Method in Soliton Theory (Cambridge Univ. Press, New York, 2004). · Zbl 1099.35111 |
| [20] | Hu, L.et al., Mod. Phys. Lett. B33, 1950376 (2019). |
| [21] | Luo, L., Appl. Math. Lett.94, 94 (2019). · Zbl 1412.35055 |
| [22] | Jia, T. T.et al., Appl. Math. Lett.114, 106702 (2021). |
| [23] | Du, Z. and Ma, Y. P., Appl. Math. Lett.116, 106999 (2021). · Zbl 1481.35113 |
| [24] | Guan, X.et al., Nonlinear Dyn.98, 1491 (2019). |
| [25] | Deng, G. F.et al., Chaos Solitons Fract.140, 110085 (2020). |
| [26] | Gürses, M. and Pekcan, A., Commun. Nonlinear Sci. Numer. Simulat.67, 427 (2019). · Zbl 1508.35121 |
| [27] | Li, L. Q.et al., Nonlinear Dyn.100, 2729 (2020). |
| [28] | Deng, G. F.et al., Nonlinear Dyn.99, 1039 (2020). |
| [29] | Zhang, X. and Chen, Y., Appl. Math. Lett.98, 306 (2019). · Zbl 1428.35547 |
| [30] | Gao, X. Y., Guo, Y. J. and Shan, W. R., Appl. Math. Lett.104, 106170 (2020). · Zbl 1437.86001 |
| [31] | Liu, F. Y.et al., Chaos Solitons Fract.144, 110559 (2021). |
| [32] | Kumar, S. and Kumar, D., Comput. Math. Appl.77, 2096 (2019). · Zbl 1442.35382 |
| [33] | Ding, C. C., Gao, Y. T. and Deng, G. F., Nonlinear Dyn.97, 2023 (2019). |
| [34] | Feng, Y. J.et al., Mod. Phys. Lett. B33, 1950354 (2019). |
| [35] | Gao, X. Y., Guo, Y. J. and Shan, W. R., Chaos Solitons Fract.138, 109950 (2020). · Zbl 1490.35314 |
| [36] | Feng, L. L. and Zhang, T. T., Appl. Math. Lett.78, 133 (2018). · Zbl 1384.35119 |
| [37] | Seadawy, A. R., Eur. Phys. J. Plus132, 29 (2017). |
| [38] | Wang, P., Li, Y. L. and Qi, F. H., Appl. Math. Lett.102, 106139 (2020). · Zbl 1440.35032 |
| [39] | Yuan, F., Cheng, Y. and He, J. S., Commun. Nonlinear Sci. Numer. Simulat.83, 105027 (2020). · Zbl 1456.35183 |
| [40] | Ma, W. X., Phys. Lett. A379, 1975 (2015). · Zbl 1364.35337 |
| [41] | Wang, P.et al., Comp. Math. Math. Phys.60, 1480 (2020). |
| [42] | Weiss, J., Tabor, M. and Carnevale, G., J. Math. Phys.24, 522 (1983). · Zbl 0514.35083 |
| [43] | Hu, W. Q.et al., Wave. Random Complex27, 458 (2017). |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
