Multiple rogue wave solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation. (English) Zbl 07848656
Summary: In this paper, a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation are investigated. The first-order, second-order and third-order rogue wave solutions of this equation are derived based on a symbolic computation approach. Their dynamics features are shown in some 3D and contour plots. Compared with the previous literatures, our work does not require the Hirota bilinear form of the equation.
MSC:
| 35C08 | Soliton solutions |
| 68M07 | Mathematical problems of computer architecture |
| 33F10 | Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) |
References:
| [1] | Lan, Z. Z.; Su, J. J., Solitary and rogue waves with controllable backgrounds for the non-autonomous generalized AB system, Nonlinear Dyn., 96, 2535-2546, 2019 · Zbl 1468.76017 |
| [2] | Liu, J. G.; Eslami, M.; Rezazadeh, H.; Mirzazadeh, M., Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev-Petviashvili equation, Nonlinear Dyn., 95, 1027-1033, 2019 · Zbl 1439.35418 |
| [3] | Yin, Y. H.; Ma, W. X.; Liu, J. G.; Lü, X., Diversity of exact solutions to a (3+1)-dimensional nonlinear evolution equation and its reduction, Comput. Math. Appl., 76, 1275-1283, 2018 · Zbl 1434.35172 |
| [4] | Yang, M., Abundant exact solutions for the (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients, Chin. J. Phys., 65, 491-499, 2020 · Zbl 07832471 |
| [5] | Lü, X.; Lin, F. H.; Qi, F. H., Analytical study on a two-dimensional Korteweg-de Vries model with bilinear representation, Bäcklund transformation and soliton solutions, Appl. Math. Model., 39, 3221-3226, 2015 · Zbl 1443.35135 |
| [6] | Lan, Z. Z., Soliton and breather solutions for a fifth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber, Appl. Math. Lett., 102, 106132, 2020 · Zbl 1440.35029 |
| [7] | Lan, Z. Z., Pfaffian and extended Pfaffian solutions for a (3+1)-dimensional generalized wave equation, Phys. Scr., 94, 125221, 2019 |
| [8] | Liu, J. G., Lump-type solutions and interaction solutions for the (2+1)-dimensional generalized fifth-order KdV equation, Appl. Math. Lett., 86, 36-41, 2018 · Zbl 1410.35175 |
| [9] | Liu, J. G.; Osman, M. S.; Zhu, W. H.; Zhou, L.; Ai, G. P., Different complex wave structures described by the Hirota equation with variable coefficients in inhomogeneous optical fibers, Appl. Phys. B, 125, 175, 2019 |
| [10] | Kaur, L.; Wazwaz, A. M., Dynamical analysis of lump solutions for (3 + 1) dimensional generalized KP-boussinesq equation and its dimensionally reduced equations, Phys. Scr., 93, 7, 075203, 2018 |
| [11] | Huang, L. L.; Chen, Y., Localized excitations and interactional solutions for the reduced Maxwell-Bloch equations, Commun. Nonlinear Sci., 67, 237-252, 2019 · Zbl 1508.78002 |
| [12] | Osman, M. S., On multi-soliton solutions for the (2+1)-dimensional breaking soliton equation with variable coefficients in a graded-index waveguide, Comput. Math. Appl., 75, 1, 1-6, 2018 · Zbl 1418.35328 |
| [13] | Li, Y. Z.; Liu, J. G., New periodic solitary wave solutions for the new (2+1)-dimensional Korteweg-de Vries equation, Nonlinear Dyn., 91, 1, 497-504, 2018 |
| [14] | Liu, J. G.; He, Y., Abundant lump and lump-kink solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, Nonlinear Dyn., 92, 3, 1103-1108, 2018 |
| [15] | Yu, M. X.; Tian, B.; Yuan, Y. Q.; Sun, Y.; Du, X. X., Conservation laws, solitons, breather and rogue waves for the (2+1)-dimensional variable-coefficient Nizhnik-Novikov-Veselov system in an inhomogeneous medium, Chin. J. Phys., 56, 2, 645-658, 2018 · Zbl 07818825 |
| [16] | Hu, C. C.; Tian, B.; Wu, X. Y.; Du, Z.; Zhao, X. H., Lump wave-soliton and rogue wave-soliton interactions for a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation in a fluid, Chin. J. Phys., 56, 2395-2403, 2018 · Zbl 07820742 |
| [17] | Rahman, M. H.; Chowdhury, N. A.; Mannan, A., Modulational instability, rogue waves, and envelope solitons in opposite polarity dusty plasmas, Chin. J. Phys., 56, 5, 2061-2068, 2018 |
| [18] | Wang, M.; Tian, B.; Sun, Y.; Yin, H. M.; Zhang, Z., Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev-Petviashvili equation in fluid mechanics, Chin. J. Phys., 60, 440-449, 2019 · Zbl 07823604 |
| [19] | Liu, J. G.; Zhu, W. H., Multiple rogue wave solutions for (2+1)-dimensional Boussinesq equation, Chin. J. Phys., 67, 492-500, 2020 · Zbl 07833201 |
| [20] | Elboree, M. K., Lump solitons, rogue wave solutions and lump-stripe interaction phenomena to an extended (3+1)-dimensional KP equation, Chin. J. Phys., 63, 290-303, 2020 · Zbl 07829574 |
| [21] | Lan, Z. Z., Rogue wave solutions for a higher-order nonlinear Schrödinger equation in an optical fiber, Appl. Math. Lett., 107, 106382, 2020 · Zbl 1442.35424 |
| [22] | Yin, Y.; Tian, B.; Wu, Y. Y.; Yin, H. M.; Zhang, C. L., Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation for an offshore structure, Mod. Phys. Lett. B, 32, 10, 1850031, 2018 |
| [23] | Mekki, A.; Ali, M. M., Numerical simulation past of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equations using finite difference method, Appl. Math. Comput., 219, 11214-11222, 2013 · Zbl 1304.65193 |
| [24] | Tariq, U. H.; Seadawy, A. R., Soliton solutions of (3 + 1)-dimensional Korteweg-de Vries Benjamin-Bona-Mahony, Kadomtsev-Petviashvili Benjamin-Bona-Mahony and modified Korteweg de Vries-Zakharov-Kuznetsov equations and their applications in water waves, J. King Saud Univ. Sci., 31, 8-13, 2019 |
| [25] | Zha, Q. L., A symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems, Comput. Math. Appl., 75, 9, 3331-3342, 2018 · Zbl 1409.76017 |
| [26] | Liu, W. H.; Zhang, Y. F., Multiple rogue wave solutions for a (3+1)-dimensional Hirota bilinear equation, Appl. Math. Lett., 98, 184-190, 2019 · Zbl 1426.35085 |
| [27] | Zhao, Z. L.; He, L. C.; Gao, Y. B., Rogue wave and multiple lump solutions of the (2+1)-dimensional Benjamin-Ono equation in fluid mechanics, Complexity, 2019, 8249635, 2019 · Zbl 1434.35133 |
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