\(M\)-lump and hybrid solutions of a generalized \((2+1)\)-dimensional Hirota-Satsuma-Ito equation. (English) Zbl 1450.35116
Summary: In this paper, the \(N\)-soliton solutions of a generalized \((2+1)\)-dimensional Hirota-Satsuma-Ito equation are obtained by means of the bilinear method. By applying the long wave limit to the \(N\)-solitons, the \(M\)-lump waves are constructed. The propagation orbits, velocities and the collisions among the lumps of the \(M\)-lump waves are analyzed. Three kinds of high-order hybrid solutions are presented, which contain the hybrid solution between lumps and solitons, a 1-lump and 1-breather, and a \(m\)-breather and \(n\)-soliton. The results are helpful to explain some nonlinear phenomena of the generalized shallow water wave model.
MSC:
35C08 | Soliton solutions |
35C07 | Traveling wave solutions |
35G25 | Initial value problems for nonlinear higher-order PDEs |
35Q35 | PDEs in connection with fluid mechanics |
References:
[1] | Ma, W. X., Phys. Lett. A, 379, 1975-1978 (2015) · Zbl 1364.35337 |
[2] | Sun, Y. L.; Ma, W. X.; Yu, J. P., Math. Methods Appl. Sci., 43, 6276-6282 (2020) · Zbl 1451.35175 |
[3] | Zhao, Z. L.; Chen, Y.; Han, B., Modern Phys. Lett. B, 31, Article 1750157 pp. (2017) |
[4] | Zhao, Z. L.; Han, B., Anal. Math. Phys., 9, 119-130 (2019) · Zbl 1418.35082 |
[5] | Wang, X. B.; Tian, S. F.; Qin, C. Y.; Zhang, T. T., Appl. Math. Lett., 68, 40-47 (2017) · Zbl 1362.35086 |
[6] | Manakov, S. V.; Zakharov, V. E.; Bordag, L. A.; Its, A. R.; Matveev, V. B., Phys. Lett. A, 63, 205-206 (1977) |
[7] | Satsuma, J.; Ablowitz, M. J., J. Math. Phys., 20, 1496-1503 (1979) · Zbl 0422.35014 |
[8] | Zhang, Y.; Liu, Y. P.; Tang, X. Y., Comput. Math. Appl., 76, 592-601 (2018) · Zbl 1420.35335 |
[9] | Zhang, Y.; Liu, Y. P.; Tang, X. Y., Nonlinear Dynam., 93, 2533-2541 (2018) · Zbl 1398.35014 |
[10] | An, H. L.; Feng, D. L.; Zhu, H. X., Nonlinear Dynam., 98, 1275-1286 (2019) |
[11] | Tan, W.; Dai, Z. D.; Yin, Z. Y., Nonlinear Dynam., 96, 1605-1614 (2019) · Zbl 1437.35612 |
[12] | Manafian, J.; Lakestani, M., J. Geom. Phys., 150, Article 103598 pp. (2020) · Zbl 1437.35148 |
[13] | Guo, H. D.; Xia, T. C.; Hu, B. B., Appl. Math. Lett., 105, Article 106301 pp. (2020) · Zbl 1436.35066 |
[14] | Zhang, Z.; Yang, S. X.; Li, B., Chin. Phys. Lett., 36, Article 120501 pp. (2019) |
[15] | Yang, X. Y.; Fan, R.; Li, B., Phys. Scr., 95, Article 045213 pp. (2020) |
[16] | Zhao, Z. L.; He, L. C., Nonlinear Dynam., 100, 2753-2765 (2020) · Zbl 1516.37123 |
[17] | Clarkson, P. A.; Dowie, E., Trans. Math. Appl., 1, 1-26 (2017) · Zbl 1403.37073 |
[18] | Zhaqilao, P. A., Comput. Math. Appl., 75, 3331-3342 (2018) · Zbl 1409.76017 |
[19] | Zhao, Z. L.; He, L. C., Appl. Math. Lett., 95, 114-121 (2019) · Zbl 1448.35418 |
[20] | Zhao, Z. L.; He, L. C.; Gao, Y. B., Complexity, 2019, Article 8249635 pp. (2019) · Zbl 1434.35133 |
[21] | He, L. C.; Zhao, Z. L., Modern Phys. Lett. B, 33, Article 2050167 pp. (2020) |
[22] | Kuo, C. K.; Ghanbari, B., Nonlinear Dynam., 96, 459-464 (2019) · Zbl 1437.37093 |
[23] | Wazwaz, A. M., Appl. Math. Lett., 64, 21-26 (2017) · Zbl 1353.65109 |
[24] | Zhou, Y.; Manukure, S.; Ma, W. X., Commun. Nonlinear Sci. Numer. Simul., 68, 56-62 (2019) · Zbl 1509.35101 |
[25] | Kuo, C. K.; Ma, W. X., Nonlinear Anal., 190, Article 111592 pp. (2020) · Zbl 1430.35048 |
[26] | Liu, W.; Wazwaz, A. M.; Zhang, X. X., Phys. Scr., 94, Article 075203 pp. (2019) |
[27] | Aliyu, A. I.; Li, Y. J., Eur. Phys. J. Plus, 135, 119 (2020) |
[28] | Liu, J. G.; Zhu, W. H.; Zhou, L., Eur. Phys. J. Plus, 135, 20 (2020) |
[29] | Liu, Y. Q.; Wen, X. Y.; Wang, D. S., Comput. Math. Appl., 77, 947-966 (2019) · Zbl 1442.35390 |
[30] | Chen, S. J.; Ma, W. X.; Lü, X., Commun. Nonlinear Sci. Numer. Simul., 83, Article 105135 pp. (2020) · Zbl 1456.35178 |
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