Lump, breather and interaction solutions to the (3+1)-dimensional generalized Camassa-Holm Kadomtsev-Petviashvili equation. (English) Zbl 1530.35210
Summary: This paper analyzes the (3+1)-dimensional generalized Camassa-Holm Kadomtsev-Petviashvili(gCH-KP) equation, which has recently gained popularity in ocean physics and hydrodynamics engineering. Based on the Hirota bilinear method and symbolic computation, we explore the lump solution, breather solution and new interaction solutions. The maximum and minimum value of the lump solution are obtained by theoretical calculation. Dynamic characteristics of these solutions are depicted by presenting some three dimensional, two dimensional plots and density plots.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q51 | Soliton equations |
| 76B25 | Solitary waves for incompressible inviscid fluids |
| 35C08 | Soliton solutions |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
(3+1)-dimensional gCH-KP equation; Hirota bilinear method; lump solution; interaction solutionsReferences:
| [1] | Abdou, M., Further improved f-expansion and new exact solutions for nonlinear evolution equations, Nonlinear Dyn., 52, 3, 277-288 (2008) · Zbl 1173.35648 |
| [2] | Chen, S.-J.; Yin, Y.-H.; Ma, W.-X.; Lü, X., Abundant exact solutions and interaction phenomena of the (2+1)-dimensional ytsf equation, Anal. Math. Phys., 9, 2329-2344 (2019) · Zbl 1448.35441 |
| [3] | de Monvel, A. B.; Shepelsky, D., Riemann-Hilbert approach for the Camassa-Holm equation on the line, C. R. Math., 343, 10, 627-632 (2006) · Zbl 1110.35056 |
| [4] | de Monvel, A. B.; Shepelsky, D., A Riemann-Hilbert approach for the Degasperis-Procesi equation, Nonlinearity, 26, 7, 2081 (2013) · Zbl 1291.35326 |
| [5] | Dhiman, S. K.; Kumar, S., Different dynamics of invariant solutions to a generalized (3+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation arising in shallow water-waves, J. Ocean Eng. Sci. (2022) |
| [6] | Ding, C.-C.; Gao, Y.-T.; Deng, G.-F., Breather and hybrid solutions for a generalized (3+1)-dimensional b-type Kadomtsev-Petviashvili equation for the water waves, Nonlinear Dyn., 97, 4, 2023-2040 (2019) · Zbl 1430.37071 |
| [7] | Feng, Y.; Wang, X.; Bilige, S., Evolutionary behavior and novel collision of various wave solutions to (3+1)-dimensional generalized Camassa-Holm Kadomtsev-Petviashvili equation, Nonlinear Dyn., 104, 4, 4265-4275 (2021) |
| [8] | Ghanbari, B.; Liu, J.-G., Exact solitary wave solutions to the (2+1)-dimensional generalised Camassa-Holm-Kadomtsev-Petviashvili equation, Pramana, 94, 1, 1-11 (2020) |
| [9] | Hietarinta, J., Hirota’s bilinear method and soliton solutions, Physics AUC, 15, 1, 31-37 (2005) |
| [10] | Its, A., The Riemann-Hilbert problem and integrable systems, Not. Am. Math. Soc., 50, 11, 1389-1400 (2003) · Zbl 1053.34081 |
| [11] | Liu, N., Soliton and breather solutions for a fifth-order modified kdv equation with a nonzero background, Appl. Math. Lett., 104, Article 106256 pp. (2020) · Zbl 1441.35212 |
| [12] | Lu, C.; Xie, L.; Yang, H., Analysis of Lie symmetries with conservation laws and solutions for the generalized (3+1)-dimensional time fractional Camassa-Holm-Kadomtsev-Petviashvili equation, Comput. Math. Appl., 77, 12, 3154-3171 (2019) · Zbl 1442.35517 |
| [13] | Ma, W.-X., Lump solutions to the Kadomtsev-Petviashvili equation, Phys. Lett. A, 379, 36, 1975-1978 (2015) · Zbl 1364.35337 |
| [14] | Ma, W.-X., Matrix integrable fourth-order nonlinear Schrödinger equations and their exact soliton solutions, Chin. Phys. Lett., 39, 10, Article 100201 pp. (2022) |
| [15] | Ma, W.-X., Reduced non-local integrable nls hierarchies by pairs of local and non-local constraints, Int. J. Appl. Comput. Math., 8, 4, 206 (2022) · Zbl 1513.37040 |
| [16] | Ma, W.-X., Riemann-Hilbert problems and soliton solutions of type (λ*,- λ*) reduced nonlocal integrable mkdv hierarchies, Mathematics, 10, 6, 870 (2022) |
| [17] | Ma, W.-X., Matrix integrable fifth-order mkdv equations and their soliton solutions, Chin. Phys. B, 32, 2, Article 020201 pp. (2023) |
| [18] | Ma, W.-X., Sasa-Satsuma type matrix integrable hierarchies and their Riemann-Hilbert problems and soliton solutions, Phys. D: Nonlinear Phenom., 446, Article 133672 pp. (2023) · Zbl 1512.37081 |
| [19] | Osman, M.; Liu, J.-G.; Hosseini, K.; Yusuf, A., Different wave structures and stability analysis for the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation, Phys. Scr., 95, 3, Article 035229 pp. (2020) |
| [20] | Qin, C.-Y.; Tian, S.-F.; Wang, X.-B.; Zhang, T.-T., On breather waves, rogue waves and solitary waves to a generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation, Commun. Nonlinear Sci. Numer. Simul., 62, 378-385 (2018) · Zbl 1470.35124 |
| [21] | Ren, B., Cte method and interaction solutions for the Kadomtsev-Petviashvili equation, J. Korean Phys. Soc., 70, 4, 333-338 (2017) |
| [22] | Ren, B.; Lin, J.; Liu, P., Soliton molecules and the cre method in the extended mkdv equation, Commun. Theor. Phys., 72, 5, Article 055005 pp. (2020) · Zbl 1451.35173 |
| [23] | Scheider, D., Breather solutions of the cubic Klein-Gordon equation, Nonlinearity, 33, 12, 7140 (2020) · Zbl 1452.35107 |
| [24] | Wang, M.; Tian, B.; Qu, Q.-X.; Zhao, X.-H.; Zhang, Z.; Tian, H.-Y., Lump, lumpoff, rogue wave, breather wave and periodic lump solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid mechanics and plasma physics, Int. J. Comput. Math., 97, 12, 2474-2486 (2020) · Zbl 1483.35166 |
| [25] | Wang, M.; Tian, B.; Zhou, T.-Y., Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain, Chaos Solitons Fractals, 152, Article 111411 pp. (2021) · Zbl 07577316 |
| [26] | Wang, Y.-H., Cte method to the interaction solutions of Boussinesq-Burgers equations, Appl. Math. Lett., 38, 100-105 (2014) · Zbl 1314.35153 |
| [27] | Wazwaz, A.-M., The Hirota’s direct method for multiple-soliton solutions for three model equations of shallow water waves, Appl. Math. Comput., 201, 1-2, 489-503 (2008) · Zbl 1143.76018 |
| [28] | Wazwaz, A.-M., The simplified Hirota’s method for studying three extended higher-order kdv-type equations, J. Ocean Eng. Sci., 1, 3, 181-185 (2016) |
| [29] | Xu, S.; He, J.; Wang, L., The Darboux transformation of the derivative nonlinear Schrödinger equation, J. Phys. A, Math. Theor., 44, 30, Article 305203 pp. (2011) · Zbl 1221.81063 |
| [30] | Xu, T.; Wang, D.; Li, M.; Liang, H., Soliton and breather solutions of the Sasa-Satsuma equation via the Darboux transformation, Phys. Scr., 89, 7, Article 075207 pp. (2014) |
| [31] | Ye, Y.; Hou, C.; Cheng, D.; Chen, S., Rogue wave solutions of the vector Lakshmanan-Porsezian-Daniel equation, Phys. Lett. A, 384, 11, Article 126226 pp. (2020) · Zbl 1482.37072 |
| [32] | Zhang, J.-F., Homogeneous balance method and chaotic and fractal solutions for the Nizhnik-Novikov-Veselov equation, Phys. Lett. A, 313, 5-6, 401-407 (2003) · Zbl 1040.35105 |
| [33] | Zhao, X.; Wang, L.; Sun, W., The repeated homogeneous balance method and its applications to nonlinear partial differential equations, Chaos Solitons Fractals, 28, 2, 448-453 (2006) · Zbl 1082.35014 |
| [34] | Zhao, Y.-M., F-expansion method and its application for finding new exact solutions to the Kudryashov-Sinelshchikov equation, J. Appl. Math., 2013 (2013) · Zbl 1266.76056 |
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