Abstract
In this paper, we take into consideration a general form of the extended Kadomtsev–Petviashvili equation, which has several applications in applied sciences and engineering. The Painlevé analysis via WTC–Kruskal algorithm is first used to validate the integrability of this nonlinear model. Thereafter, we determine the multi-solitons, breather solutions, lump waves, rouge waves, lump with solitary waves interaction, and breather with solitons interaction by using various ansatz’s functions based on bilinear formalism and symbolic computation. The solitary wave ansatz method is used to extract the bight solitons, dark solitons, singular solitons, and the periodic function solutions. In addition, the Ma-breather, Kuznetsov–Ma breather, and their associated rogue wave solutions are also discussed. In order to demonstrate several physical structures, the figures relating to these solutions are illustrated by selecting appropriate parametric values in 2D, 3D, and contour plots with the assistance of the symbolic package Mathematica 13.1. The dynamics of nonlinear wave models are addressed by these solutions.
Similar content being viewed by others
Availability of data and materials
Not applicable.
References
Seadawy, A.R.: Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas. Phys. Plasmas 21(5), 052107 (2014)
Abdou, M.A., Zhang, S.: New periodic wave solutions via extended mapping method. Commun. Nonlinear Sci. Numer. Simul. 14(1), 2–11 (2009)
Fan, E., Zhang, H.: A note on the homogeneous balance method. Phys. Lett. A 246, 403–406 (1998)
Akinyemi, L., Şenol, M., Az-Zo’bi, E., Veeresha, P., Akpan, U.: Novel soliton solutions of four sets of generalized \((2+1)\)-dimensional Boussinesq–Kadomtsev–Petviashvili-like equations. Mod. Phys. Lett. B 36(01), 2150530 (2022)
Cheemaa, N., Seadawy, A.R., Rezazadeh, H.: Bright–dark solitary wave solutions of coupled integrable \((2+1)\)-dimensional Maccari system in applied physics. New Trends Phys. Sci. Res. 1, 31–45 (2022)
Hirota, R.: Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27(18), 1192–1194 (1971)
Hirota, R.: The Direct Method in Soliton Theory. Cambridge University Press, Cambridge (2004)
Wazwaz, A.M.: Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method. Appl. Math. Comput. 182, 283–300 (2006)
Ntiamoah, D., Ofori-Atta, W., Akinyemi, L.: The higher-order modified Kortewegde Vries equation: its soliton, breather and approximate solutions. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.06.042
Wazwaz, A.M.: Solitons and periodic solutions for the fifth-order KdV equation. Appl. Math. Lett. 19, 1162–1167 (2006)
Mirzazadeh, M., Eslami, M., Biswas, A.: Soliton solutions of the generalized Klein–Gordon equation by using \(G^{\prime }/G\)-expansion method. Comput. Appl. Math. 33(3), 831–839 (2014)
Jafari, H., Tajadodi, H., Baleanu, D.: Application of a homogeneous balance method to exact solutions of nonlinear fractional evolution equations. J. Comput. Nonlinear Dyn. 9(2), 021019–021021 (2014)
Lu, D., Zhang, Z.: Exact solutions for fractional nonlinear evolution equations by the F-expansion method. Int. J. Nonlinear Sci. 24(2), 96–103 (2017)
Akinyemi, L., Hosseini, K., Salahshour, S.: The bright and singular solitons of \((2+1)\)-dimensional nonlinear Schrödinger equation with spatio-temporal dispersions. Optik 242, 167120 (2021)
Rezazadeh, H.: New solitons solutions of the complex Ginzburg–Landau equation with Kerr law nonlinearity. Optik 167, 218–227 (2018)
Zhang, S., Xia, T.: A generalized new auxiliary equation method and its applications to nonlinear partial differential equations. Phys. Lett. A 363(5–6), 356–360 (2007)
Mathanaranjan, T., Kumar, D., Rezazadeh, H., Akinyemi, L.: Optical solitons in metamaterials with third and fourth order dispersions. Opt. Quantum Electron. 54(5), 1–15 (2022)
Eslami, M., Rezazadeh, H.: The first integral method for Wu–Zhang system with conformable time-fractional derivative. Calcolo 53(3), 475–485 (2016)
Manukure, S., Booker, T.: A short overview of solitons and applications. Partial Differ. Equ. Appl. Math. 4, 100140 (2021)
Kuwayama, H., Ishida, S.: Biological soliton in multicellular movement. Sci. Rep. 3(1), 1–5 (2013)
Davydov, A.S.: Solitons in molecular systems. Phys. Scr. 20, 387–394 (1979)
Careri, G., Wyman, J.: Soliton-assisted unidirectional circulation in a biochemical cycle. Proc. Natl. Acad. Sci. 81, 4386–4388 (1984)
Abbagari, S., Houwe, A., Akinyemi, L., Saliou, Y., Bouetou, T.B.: Modulation instability gain and discrete soliton interaction in gyrotropic molecular chain. Chaos Solitons Fractals 160, 112255 (2022)
Yu, J., Wang, F., Ma, W., Sun, Y., Khalique, C.M.: Multiple-soliton solutions and lumps of a \((3+1)\)-dimensional generalized KP equation. Nonlinear Dyn. 95(2), 1687–1692 (2019)
Li, B.Q., Ma, Y.L.: Multiple-lump waves for a \((3+1)\)-dimensional Boiti–Leon–Manna–Pempinelli equation arising from incompressible fluid. Comput. Math. Appl. 76(1), 204–214 (2018)
Ma, Y.L., Li, B.Q.: Analytic rogue wave solutions for a generalized fourth-order Boussinesq equation in fluid mechanics. Math. Methods Appl. Sci. 42, 39–48 (2019)
Wang, C.J., Fang, H., Tang, X.X.: State transition of lump-type waves for the \((2+1)\)-dimensional generalized KdV equation. Nonlinear Dyn. 95, 2943–2961 (2019)
Houwe, A., Souleymanou, A., Akinyemi, L., Doka, S.Y., Inc, M.: Discrete breathers incited by the intra-dimers parameter in microtubulin protofilament array. Eur. Phys. J. Plus 137(4), 1–7 (2022)
Chabchoub, A., Kibler, B., Dudley, J.M., Akhmediev, N.: Hydrodynamics of periodic breathers. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 372(2027), 4152–4160 (2014)
Wazwaz, A.M.: Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method. Appl. Math. Comput. 190(1), 633–640 (2007)
Biondini, G., Kodama, Y.: On a family of solutions of the Kadomtsev–Petviashvili equation which also satisfy the Toda lattice hierarchy. J. Phys. A: Math. Gen. 36(42), 10519 (2003)
Biondini, G., Chakravarty, S.: Soliton solutions of the Kadomtsev–Petviashvili II equation. J. Math. Phys. 47(3), 1–26 (2006)
Dai, Z., Lin, S., Fu, H., Zeng, X.: Exact three-wave solutions for the KP equation. Appl. Math. Comput. 216(5), 1599–1604 (2010)
Manukure, S., Zhou, Y., Ma, W.X.: Lump solutions to a \((2+1)\)-dimensional extended KP equation. Comput. Math. Appl. 75, 2414–2419 (2018)
Peckan, A.: The Hirota Direct Method (Masters thesis), Bilkent University (2005)
Ahmed, I., Seadawy, A.R., Lu, D.: Mixed lump-solitons, periodic lump and breather soliton solutions for \((2+1)\)-dimensional extended Kadomtsev–Petviashvili dynamical equation. Int. J. Mod. Phys. B 33(05), 1950019 (2019)
Guo, J., He, J., Li, M., Mihalache, D.: Exact solutions with elastic interactions for the \((2+1)\)-dimensional extended Kadomtsev–Petviashvili equation. Nonlinear Dyn. 101(4), 2413–2422 (2020)
Guo, J., He, J., Li, M., Mihalache, D.: Exact solutions with elastic interactions for the \((2+1)\)-dimensional extended Kadomtsev–Petviashvili equation. Nonlinear Dyn. 101, 2413–2422 (2020)
Wazwaz, A.M.: Extended KP equations and extended system of KP equations: multiple-soliton solutions. Can. J. Phys. 89, 739–743 (2011)
Guan, X., Liu, W., Zhou, Q., Biswas, A.: Some lump solutions for a generalized \((3+1)\)-dimensional Kadomtsev–Petviashvili equation. Appl. Math. Comput. 366, 124757 (2020)
Ma, Y.L., Wazwaz, A.M., Li, B.Q.: New extended Kadomtsev–Petviashvili equation: multiple soliton solutions, breather, lump and interaction solutions. Nonlinear Dyn. 104(2), 1581–1594 (2021)
Li, L., Xie, Y., Yan, Y., Wang, M.: A new extended \((2+1)\)-dimensional Kadomtsev–Petviashvili equation with N-solitons, periodic solutions, rogue waves, breathers and lump waves. Results Phys 39, 105678 (2022)
Fordy, A., Pickering, A.: Analysing negative resonances in the Painlevé test. Phys. Lett. A 160(4), 347–354 (1991)
Xu, G.: The soliton solutions, dromions of the Kadomtsev–Petviashvili and Jimbo–Miwa equations in \((3+1)\)-dimensions. Chaos Solitons Fractals 30(1), 71–76 (2006)
Ma, Y.L.: N-solitons, breathers and rogue waves for a generalized Boussinesq equation. Int. J. Comput. Math. 97(8), 1648–1661 (2020)
Acknowledgements
The authors would like to thank the EXCEL Scholars Program and the Department of Mathematics at Lafayette College for their support of this project.
Funding
No funding available for this project.
Author information
Authors and Affiliations
Contributions
The authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Ethics approval
Not applicable
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Akinyemi, L., Morazara, E. Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev–Petviashvili equation. Nonlinear Dyn 111, 4683–4707 (2023). https://doi.org/10.1007/s11071-022-08087-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-022-08087-x