Abstract
The analytical study of Boiti-Leon-Manna-Pempinelli (BLMP) equation is presented in this research paper. In this study, two exact methods are utilized to attain the exact solution of proposed equation. The generalized projective Riccati equations method and modified auxiliary equation method are simple and effective techniques, which have been used to attain the exact soliton solutions of BLMP equation. Some novel exact solution of BLMP equation are acquired using of proposed methods. The obtained solutions contain rational, geometric, hyperbolic functions. The graphical simulations of attained solutions are represented by plotted graphs. The plotted graphs show different solitons patterns such as kink solitons, anti-kink soliton, dark singular soliton, bright singular soliton, dark-bright singular solition and some other singular solitons. Mathematical modeling, analysis of physical phenomena and dynamical processes can yield solutions that enhance our understanding of their dynamics, which can be leveraged to gain valuable insights into the behavior and characteristics of these systems.
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References
Akbar, M.A., Abdullah, F.A., Islam, M.T., Al-Sharif, M.A., Osman, M.S.: New solutions of the soliton type of shallow water waves and superconductivity models. Res. Phys. 44, 106180 (2023)
Akram, G., Sadaf, M., Arshed, S., Sameen, F.: Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan-Porsezian-Daniel model by generalized projective Riccati equations method. Optik 241, 167051 (2021)
Akram, G., Sadaf, M., Khan, M.A.U.: Soliton solutions of Lakshmanan-Porsezian-Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities. Optik 252, 168372 (2022a)
Akram, G., Sadaf, M., Khan, M.A.U.: Soliton dynamics of the generalized shallow water like equation in nonlinear phenomenon. Front. Phys. 10, 82204 (2022b)
Akram, G., Sadaf, M., Khan, M.A.U.: Dynamics investigation of the \((4+ 1)\)-dimensional Fokas equation using two effective techniques. Res. Phys. 42, 105994 (2022c)
Akram, G., Sadaf, M., Khan, M.A.U.: Soliton solutions of the resonant nonlinear Schrödinger equation using modified auxiliary equation method with three different nonlinearities. Math. Comput. Simul. 206, 1–20 (2023)
Arafat, S.M.Y., Fatema, K., Islam, M.E., Akbar, M.A.: Promulgation on various genres soliton of Maccari system in nonlinear optics. Opt. Quantum Electron. 54(4), 206 (2022)
Arafat, S.M.Y., Fatema, K., Islam, S.M.R., Islam, M.E., Akbar, M.A., Osman, M.S.: The mathematical and wave profile analysis of the Maccari system in nonlinear physical phenomena. Opt. Quantum Electron. 55(2), 136 (2023)
Butt, A.R., Raza, N., Inc, M., Alqahtani, R.T.: Complexitons, Bilinear forms and Bi$$(2+ 1)$$linear Bäcklund transformation of a \((2+ 1)\)-dimensional Boiti-Leon-Manna-Pempinelli model describing incompressible fluid. Chaos Solitons Fractals 168, 113201 (2023)
Fatema, K., Islam, Md.E., Arafat, S.M.Y., Akbar, M.A.: Solitons behavior of waves by the effect of linearity and velocity of the results of a model in magnetized plasma field. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.07.003
Hao, Q.: Exact solution of \((4+ 1)\)-dimensional Boiti–Leon–Manna–Pempinelli equation. Adv. Math. Phys. (2023)
Islam, Md.T., Akter, M.A., Ryehan, S., Gómez-Aguilar, J.F., Akbar, M.A.: A variety of solitons on the oceans exposed by the Kadomtsev Petviashvili-modified equal width equation adopting different techniques. J. Ocean Eng. Sci. 7(6), 528–535 (2022)
Islam, M.E., Akbar, M.A.A.: Study of the parametric effects on soliton propagation in optical fibers through two analytical methods. Opt. Quantum Electron. 53, 1–20 (2021)
Islam, M.E., Barman, H.K., Akbar, M.A.: Search for interactions of phenomena described by the coupled Higgs field equation through analytical solutions. Opt. Quantum Electron. 52, 1–19 (2020)
Islam, M.T., Akbar, M.A., Gómez-Aguilar, J.F., Bonyah, E., Fernandez-Anaya, G.: Assorted soliton structures of solutions for fractional nonlinear Schrödinger types evolution equations. J. Ocean Eng. Sci. 7(6), 528–535 (2022)
Islam, M.E., Hossain, M.M., Helal, K.M., Basak, U.S., Bhowmik, R.C., Akbar, M.A.: Solitary wave analysis of the Kadomtsev-Petviashvili model in mathematical physics. Arab J. Basic Appl. Sci. 30(1), 329–340 (2023a)
Islam, M.T., Sarkar, T.R., Abdullah, F.A., Gómez-Aguilar, J.F.: Characteristics of dynamic waves in incompressible fluid regarding nonlinear Boiti-Leon-Manna-Pempinelli model. Phys. Scr. 98(8), 085230 (2023b)
Islam, Md.T., Akter, M.A., Gomez-Aguilar, J.F., Akbar, Md.A., Pérez-Careta, E.: Innovative and diverse soliton solutions of the dual core optical fiber nonlinear models via two competent techniques. J. Nonlinear Opt. Phys. Mater. 32, 2350037 (2023c)
Islam, M.T., Ryehan, S., Abdullah, F.A., Gómez-Aguilar, J.F.: The effect of Brownian motion and noise strength on solutions of stochastic Bogoyavlenskii model alongside conformable fractional derivative. Optik 287, 171140 (2023d)
Khater, M.M.A., Seadawy, A.R., Lu, D.: Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-pempinelli equations system and Time-fractional Cahn-Allen equation. Res. Phys. 7, 2325–2333 (2017)
Khater, M.M.A., Attia, R.A.M., Lu, D.: Modified auxiliary equation method versus three nonlinear fractional biological models in present explicit wave solutions. Math. Comput. Appl. 24(1), 1 (2018)
Osman, M.S., Lu, D., Khater, M.M.A., Attia, R.A.M.: Complex wave structures for abundant solutions related to the complex Ginzburg-Landau model. Optik 192, 162927 (2019)
Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T.A.: Optical solitons and other solutions to the Hirota-Maccari system with conformable, M-truncated and \(\beta\)-derivatives. Mod. Phys. Lett. B 36(11), 2150625 (2022)
Rani, M., Ahmed, N., Dragomir, S.S., Mohyud-Din, S.T.: Traveling wave solutions of (3+ 1)-dimensional Boiti-Leon-Manna-Pempinelli equation by using improved \(\tanh (\frac{\phi }{2})\)-expansion method. Partial Differ. Equ. Appl. Math. 6, 100394 (2022)
Rezazadeh, H., Korkmaz, A., Eslami, M., Vahidi, J., Asghari, R.: Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method. Opt. Quantum Electron. 50, 1–13 (2018)
Tang, Y., Zai, W.: New periodic-wave solutions for \((2+ 1)\) and \((3+ 1)\)-dimensional Boiti-Leon-Manna-Pempinelli equations. Nonlinear Dyn. 81, 249–255 (2015)
Tariq, K.U., Bekir, A., Zubair, M.: On some new travelling wave structures to the \((3+ 1)\)-dimensional Boiti-Leon-Manna-Pempinelli model. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.03.015
Wu, J., Liu, Y., Piao, L., Zhuang, J., Wang, D.S.: Nonlinear localized waves resonance and interaction solutions of the \((3+ 1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation. Nonlinear Dyn. 100, 1527–1541 (2020)
Yokuş, A., Durur, H., Duran, S., Islam, M.T.: Ample felicitous wave structures for fractional foam drainage equation modeling for fluid-flow mechanism. Comput. Appl. Math. 41(4), 174 (2022)
Younas, U., Sulaiman, T.A., Ren, J.: Dynamics of optical pulses in dual-core optical fibers modelled by decoupled nonlinear Schrödinger equation via GERF and NEDA techniques. Opt. Quantum Electron. 54(11), 738 (2022)
Yuan, N.: Rich analytical solutions of a new \((3+ 1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation. Res. Phys. 22, 103927 (2021)
Zhang, R.F., Li, M.C., Cherraf, A., Vadyala, S.R.: The interference wave and the bright and dark soliton for two integro-differential equation by using BNNM. Nonlinear Dyn. 111(9), 8637–8646 (2023)
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Akram, G., Sadaf, M. & Atta Ullah Khan, M. Analytical study of Boiti-Leon-Manna-Pempinelli equation using two exact methods. Opt Quant Electron 56, 909 (2024). https://doi.org/10.1007/s11082-024-06634-x
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DOI: https://doi.org/10.1007/s11082-024-06634-x