Mixed lump-solitons, periodic lump and breather soliton solutions for \((2 + 1)\)-dimensional extended Kadomtsev-Petviashvili dynamical equation. (English) Zbl 1423.35330
Summary: In this study, based on the Hirota bilinear method, mixed lump-solitons, periodic lump and breather soliton solutions are derived for \((2 + 1)\)-dimensional extended KP equation with the aid of symbolic computation. Furthermore, dynamics of these solutions are explained with 3d plots and 2d contour plots by taking special choices of the involved parameters. Through the mixed lump-soliton solutions, we observe two fusion phenomena, first from interaction of lump and single soliton and other from interaction of lump with two solitons. In both cases, lump moves gradually towards soliton and transfers energy until it completely merges with the solitons. We also observe new characteristics of periodic lump solutions and kinky breather solitons.
Keywords:
mixed lump-solitons solutions; periodic lump solutions; breathers; Hirota’s bilinear form; \((2 + 1)\)-dimensional extended KP equationReferences:
| [1] | Zheng, S. M., Nonlinear Evolution Equations (CRC Press, Chapman & Hall, USA, 2004). · Zbl 1085.47058 |
| [2] | Ablowitz, M. J.et al., Phys. Rev. Lett.31, 125 (1973). · Zbl 1243.35143 |
| [3] | Zeng, Z. F., Liu, J. G. and Nie, B., Nonlinear Dyn.86, 667 (2016). |
| [4] | Wazwaz, A.-M. and Kaur, L., Phys. Scr.93, 115201 (2018). |
| [5] | Kaur, L. and Gupta, R. K., Appl. Math. Comput.231, 560 (2014). · Zbl 1410.35228 |
| [6] | Kaur, L. and Gupta, R. K., Math. Meth. Appl. Sci.36, 584 (2013). · Zbl 1282.35335 |
| [7] | Kaur, L. and Gupta, R. K., Phys. Script.87, 035003 (2013). · Zbl 1266.83056 |
| [8] | Lu, D., Seadawy, A. and Arshad, M., Optik140, 136 (2017). |
| [9] | Seadawy, A. and Lu, D., Res. Phys.7, 43 (2017). |
| [10] | Wang, X.-B., Zhang, T.-T. and Dong, M.-J., Appl. Math. Lett.86, 298 (2018). · Zbl 1410.35216 |
| [11] | Feng, L.-L. and Zhang, T.-T., Appl. Math. Lett.78, 133 (2018). · Zbl 1384.35119 |
| [12] | Tian, S.-F., Appl. Math. Lett.83, 65 (2018). · Zbl 1482.35044 |
| [13] | Hirota, R., The Direct Method in Soliton Theory, Vol. 155 (Cambridge University Press, UK, 2004). · Zbl 1099.35111 |
| [14] | Yan, X.-W.et al., Comput. Math. Appl.76, 179 (2018). |
| [15] | Qin, C.-Y.et al., Comput. Math. Appl.75, 4221 (2018). |
| [16] | Yan, X.-W.et al., Z. Naturforsch. A73, 399 (2018). |
| [17] | Tian, S.-F., J. Diff. Eq.262, 506 (2017). · Zbl 1432.35194 |
| [18] | Dai, C., Wang, Y. and Zhang, J., Opt. Lett.35, 1437 (2010). |
| [19] | Liu, J. G.et al., Chaos.26, 103114 (2016). |
| [20] | Wang, C. J.et al., Commun. Theor. Phys.52, 862 (2009). |
| [21] | Seadawy, A. R., Eur. Phys. J. Plus132, 29 (2017). |
| [22] | Seadawy, A. R., Pramana J. Phys.89, 49 (2017). |
| [23] | Seadawy, A. R., Optik139, 31 (2017). |
| [24] | Seadawy, A. R., Int. J. Comput. Meth.15(03), 1850017 (2018), · Zbl 1404.76052 |
| [25] | Khater, A. H.et al., Eur. Phys. J. D39, 237 (2006). |
| [26] | Seadawy, A. R., Math. Meth. Appl. Sci.40(5), 1598 (2017). · Zbl 1366.35141 |
| [27] | Huang, L., Yue, Y. and Chen, Y., Comput. Math. Appl., in Press (2018). |
| [28] | Hu, C. C.et al., Eur. Phys. J. Plus133, 40 (2018). |
| [29] | Liu, J. G. and He, Y., Nonlinear Dyn.92, 1103 (2018). |
| [30] | Zhang, Y., Liu, Y. and Tang, X., Nonlinear Dyn.83, 117 (2018). |
| [31] | Wang, Y. H.et al., Nonlinear Dyn.92, 487 (2018). |
| [32] | Seadawy, A. R. and El-Rashidy, K., J. Phys.87, 20 (2016). |
| [33] | Das, G. C. and Sarma, J., Chaos Solitons Fractals9, 901 (1998). · Zbl 0948.76092 |
| [34] | Peng, W.-Q., Tian, S.-F. and Zhang, T.-T., Phys. Lett. A382, 2701 (2018). · Zbl 1404.35396 |
| [35] | Qin, C.-Y.et al., Comput. Math. Appl.75, 4221 (2018). |
| [36] | Yan, X.-W.et al., Nonlinear Dyn.92, 709 (2018). |
| [37] | Wang, X.-B.et al., Appl. Math. Lett.72, 58 (2017). |
| [38] | Saini, N. S., Kaur, N. and Gill, T. S., Adv. Space Res.55, 2873 (2015). |
| [39] | Pakzad, H. R. and Javidan, K., Chaos, Solitons Fractals42, 2904 (2009). · Zbl 1198.76100 |
| [40] | Feng, L.-L.et al., Appl. Math. Lett.65, 90 (2017). |
| [41] | Tian, S.-F. and Zhang, H.-Q., J. Phys. A Math. Theor.45, 055203 (2012). · Zbl 1232.35144 |
| [42] | Wu, P.et al., Mod. Phys. Lett. B32, 1850106 (2018). |
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.
