Abstract
In this paper, a variety of novel exact traveling wave solutions are constructed for the \((2+1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation via analytical techniques, namely, extended rational sine-cosine method and extended rational sinh-cosh method. The physical meaning of the geometrical structures for some of these solutions is discussed. Obtained solutions are expressed in terms of singular periodic wave, solitary waves, bright solitons, dark solitons, periodic wave and kink wave solutions with specific values of parameters. For the observation of physical activities of the problem, achieved exact solutions are vital. Moreover, to find analytical solutions of the proposed equation many methods have been used but given methodologies are effective, reliable and gave more and novel exact solutions.
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References
Akram, G., Mahak, N.: Application of the first integral method for solving (1+1) dimensional cubic-quintic complex Ginzburg-Landau equation. Optik 164, 210–217 (2018)
Akram, G., Mahak, N.: Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity. Eur. Phys. J. Plus 133(6), 212–220 (2018)
Akram, G., Mahak, N.: Analytical solution of the Korteweg-de Vries equation and microtubule equation using the first integral method. Opt. Quant. Electron 50, 145 (2018)
Ali, K.K., Cattani, C., Graveomez-Aguilar, J.F., Baleanu, D., Osman, M.S.: Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model. Chaos. Solitons. Fract. 139, 110089 (2020)
Ali, K.K., Osman, M.S., Abdel-Aty, M.: New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method. Alexandria Eng. J. 59(3), 1191–1196 (2020)
Arbabi, S., Najafi, M.: Soliton solutions of nonlinear evolution equations in mathematical physics. Optik 127(10), 4270–4274 (2016)
Batool, F., Akram, G.: Application of extended Fan sub-equation method to (1+1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution. Opt. Quant. Electron 49(11), 1–9 (2017)
Boiti, M., Leon, J., Manna, M., Pempinelli, F.: On the spectral transform of a Korteweg-de Vries equation in two spatial dimension. Inverse. Probl. 2, 271–279 (1986)
Delisle, L., Mosaddeghi, M.: Classical and SUSY solutions of the Boiti-Leon-Manna-Pempinelli equation. J. Phys. A Math. Theor. 46, 115–203 (2013)
Gilson, C.R., Nimmo, J.J., Willox, C.R.: A (2+1)- dimensional generalization of the AKNS shallow water wave equation. Phys. Lett. A 180, 337–345 (1993)
Ismael, H.F., Bulut, H., Park, C., Osman, M.S.: M-lump, N-soliton solutions, and the collision phenomena for the (2+ 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Results Phys 19, 103329 (2020)
Kumar, D., Park, C., Tamanna, N., Paul, G.C., Osman, M.S.: Dynamics of two-mode Sawada-Kotera equation: mathematical and graphical analysis of its dual-wave solutions. Results Phys 19, 10358 (2020)
Liu, J., Yang, K.: The extended F-expansion method and exact solutions of nonlinear PDEs. Chaos. Solitons. Fract 22(1), 111–121 (2004)
Liu, J.G., Osman, M.S., Wazwaz, A.M.: A variety of nonautonomous complex wave solutions for the (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients in nonlinear optical fibers. Optik 180, 917–923 (2019)
Liu, J.G., Zhu, W.H., Osman, M.S., Ma, W.X.: An explicit plethora of different classes of interactive lump solutions for an extension form of 3D-Jimbo-Miwa model. Eur. Phys. J. Plus 135(5), 412 (2020)
Liu, J.G., Osman, M.S., Zhu, W.H., Zhou, L., Baleanu, D.: The general bilinear techniques for studying the propagation of mixed-type periodic and lump-type solutions in a homogenous-dispersive medium. AIP Adv. 10(10), 105325 (2020)
Luo, L.: New exact solutions and B\(\ddot{a}\)cklund transformation for Boiti-Leon-Manna-Pempinelli equation. Phys. Lett. A 375, 1059–1063 (2001)
Mahak, N., Akram, G.: Exact solitary wave solutions by extended rational sine-cosine and extended rational sinh-cosh techniques. Phys. Scripta 94(11), 115212 (2019)
Mahak, N., Akram, G.: Extension of rational sine-cosine and rational sinh-cosh techniques to extract solutions for the perturbed NLSE with Kerr law nonlinearity. Eur. Phys. J. Plus 134(40), 159–168 (2019)
Najafi, M., Najafi, M., Arbabi, S.: Wronskian determinant solutions of the (2+1)-dimensional Boiti-Leon-Manna- Pempinelli equation. Int. J. Adv. Math. Sci 1, 8–11 (2013)
Osman, M.S., Liu, J.G., Hosseini, K., Yusuf, A.: Different wave structures and stability analysis for the generalized (2+1)-dimension Camassa-Holm-Kadomtsev-Petviashvili equation. Phys. Scripta 95(3), 035229 (2020)
Osman, M.S.: Multi-soliton rational solutions for quantum Zakharov-Kuznetsov equation in quantum magnetoplasmas. Wave Random Complex 26(4), 434–443 (2016)
Osman, M.S., Ghanbari, B.: New optical solitary wave solutions of Fokas-Lenells equation in presence of perturbation terms by a novel approach. Optik 175, 328–333 (2018)
Osman, M.S., Rezazadeh, H., Eslami, M., Neirameh, A., Mirzazadeh, M.: Analytical study of solitons to benjamin-bona-mahony-peregrine equation with power law nonlinearity by using three methods. Univ. Politehnica Bucharest Sci. Bull.-Ser. -Appl. Math. Phys. 80(4), 267–278 (2018)
Sajid, N., Akram, G.: The application of the exp(\(-\phi \xi\))-expansion method for finding the exact solutions of two integrable equations. Math. Probl. Eng 2018, 1–10 (2018)
Tang, Y., Zai, W.: New periodic-wave solutions for (2+ 1)- and (3+ 1)-dimensional Boiti-Leon-Manna-Pempinelli equations. Nonlinear. Dynam 81(1–2), 249–55 (2015)
Tariq, H., Akram, G.: New approach for exact solutions of time fractional Cahn-Allen equation and time fractional Phi-4 equation. Phys. A 473, 352–362 (2017)
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Mahak, N., Akram, G. Application of extended rational trigonometric techniques to investigate solitary wave solutions. Opt Quant Electron 53, 437 (2021). https://doi.org/10.1007/s11082-021-03060-1
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DOI: https://doi.org/10.1007/s11082-021-03060-1