Abstract
In this paper, we consider the Sharma-Tasso-Olver-Like equation (STOLE) describing the dynamical behaviour of nonlinear dispersive waves in inhomogeneous medium. By using the Hirota bilinear method, some new type of solitons like breather-wave, kink solitary wave and rogue wave, one-, two- and new three-wave solutions to the STOLE have been determined. These results are achieved and verified by using the Maple software. The obtained results are new from the existing results. For the further explanation of these solutions, different kinds of graphs are also drawn. These solitons suggest that this method is effective, straight forward and reliable as compare to other methods.
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22 December 2022
A Correction to this paper has been published: https://doi.org/10.1007/s11082-022-04467-0
References
Abdou, M.A., et al.: Explicit solutions to the Sharma-Tasso-Olver equation. AIMS Math. 5(6), 7272–7284 (2020)
Alrashed, R., Alshaery, A.A., Alkhateeb, S.: Optical solitons via the collective variable method for the classical and perturbed Chen-Lee-Liu equations. Open Phys. 19(1), 559–567 (2021)
Baskonus, H.M., Osman, M.S., Rehman, H.U., Ramzan, M., Tahir, M., Ashraf, S.: On pulse propagation of soliton wave solutions related to the perturbed Chen-Lee-Liu equation in an optical fiber. Opt. Quantum Electron. 53, 556 (2021)
Bekir, A.: Application of the Exp-function method for nonlinear differential-difference equations. Appl. Math. Comput. 215(11), 4049–4053 (2010)
Bekir, A., Kaplan, M.: Exponential rational function method for solving nonlinear equations arising in various physical models. Chin. J. Phys. 54(3), 365–370 (2016)
Cevikel, A.C., Bekir, A.: New solitons and periodic solutions for (2+1)-dimensional Davey-Stewartson equations. Chin. J. Phys. 51(1), 1–13 (2013)
El-Rashidy, K.: New traveling wave solutions for the higher Sharma-Tasso-Olver equation by using extension exponential rational function method. Results Phys. 17, 1–9 (2020)
Esen, H., Ozdemir, N., Secer, A., Bayram, M.: On solitary wave solutions for the perturbed Chen-Lee-Liu equation via an analytical approach. Optik 245, 167641 (2021)
Hajiseyedazizi, S.N., et al.: On multi-step methods for singular fractional q-integro-differential equations. Open Math. 19(1), 1378–1405 (2021)
Hashemi, M.S.: Some new exact solutions of (2+ 1)-dimensional nonlinear Heisenberg ferromagnetic spin chain with the conformable time fractional derivative. Opt. Quantum Electron. 50(2), 1–11 (2018)
Hashemi, M.S., Baleanu, D.: Lie symmetry analysis of fractional differential equations, CRC Press (2020)
Hirota, R.: Direct methods in soliton theory, Cambridge University Prees, (2004)
Iqbal, M.A., Wang, Y., Miah, M.M., Osman, M.S.: Study on date-Jimbo-Kashiwara-Miwa equation with conformable derivative dependent on time parameter to find the exact dynamic wave solutions. Fractal Fract. 6, 4 (2021)
Kudryashov, N.A.: General solution of the traveling wave reduction for the perturbed Chen-Lee-Liu equation. Optik 186, 339–349 (2019)
Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equation. Optik 206, 163550 (2019)
Lian, Z.J., Lou, S.Y.: Symmetries and exact solutions of the Sharma-Tasso-Olver equation. Nonlinear Anal. 63, 1167–1177 (2005)
Liu, J.G., Du, J.Q., Zeng, Z.F., Nie, B.: New three-wave solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Nonlinear Dyn. 88, 655–661 (2017)
Li, Z., Manafian, J., Ibrahimov, N., Hajar, A., Nisar, K.S., Jamshed, W.: Variety interaction between k-lump and k-kink solutions for the generalized Burger equation with variable coefficients by bilinear analysis. Results Phys. 28, 104490 (2021)
Lü, J., Bilige, S., Gao, X., Bai, Y., Zhang, R.: Abundant lump solutions and interaction phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation. J. Appl. Math. Phys. 6, 1733–1747 (2018)
Peng, W.Q., Tian, S.F., Zhang, T.T.: Dynamics of the soliton waves, breather waves, and rogue waves to the cylindrical Kadomtsev-Petviashvili equation in pairion-electron plasma. Phys. Fluid 31, 102107 (2019a)
Peng, W.Q., Tian, S.F., Wang, X.B., Zhang, T.T., Fang, Y.: Riemann-Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrödinger equations. J. Geom. Phys. 146, 103508 (2019b)
Peng, W.Q., Tian, S.F., Zhang, T.T., Fang, Y.: Rational and semi-rational solutions of a nonlocal (2+ 1)-dimensional nonlinear Schröodinger equation. Math. Meth. Appl. Sci. 42, 6865–6877 (2019c)
Rashid, S., et al.: Some recent developments on dynamical \(\hbar \)-discrete fractional type inequalities in the frame of nonsingular and nonlocal Kernels. Fractals 30, 2240110 (2022)
Sirisubtawee, S., Koonprasert, S., Sungnul, S.: New exact solutions of the conformable space-time Sharma-Tasso-Olver equation Using two reliable methods. Symmetry 12, 1–25 (2020)
Ullah, M.S., Roshid, H., Ma, W.-X., Ali, M.Z., Rahman, Z.: Interaction phenomena among lump, periodic and kink wave solutions to a (3 + 1)-dimensional Sharma-Tasso-Olver-like equation. Chinese J. Phys. 68, 699–711 (2020)
Wang, C., Dai, Z., Liu, C.: Interaction Bbetween kink solitary wave and rogue wave for (2+1)-dimensional Burgers equation. Mediterr. J. Math. 13, 1087–1098 (2016)
Wu, X.H., He, J.H.: Exp-function method and its application to nonlinear equations. Chaos Solitons Fractals 38, 903–910 (2008)
Yépez-Martínez, H., Rezazadeh, H., Inc, M., Akinlar, M.A.: New solutions to the fractional perturbed Chen–Lee–Liu equation with a new local fractional derivative, Waves in Random and Complex Media, 1–36, (2021)
Yue, Y., Huang, L., Chen, Y.: N-solitons, breathers, lumps and rogue wave solutions to a (3+1)-dimensional nonlinear evolution equation. Comput. Math. Appl. 75, 2538–2548 (2018)
Zafar, A., Raheel, M., Bekir, A.: Expolring the dark and singular soliton solutions of Biswas-Arshed model with full nonlinear form. Optik 204, 164133 (2020)
Zhang, L.D., Tian, S.F., Peng, W.Q., Zhang, T.T., Yan, X.J.: The dynamics of lump, lump-off and rogue wave solutions of (2+1)-dimensional Hirota-Satsuma-Ito equations. East Asian J. Appl. Math. 10, 243–255 (2020)
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The authors would like to acknowledge the financial support of Taif University Researchers Supporting Project number (TURSP-2020/162), Taif University, Taif, Saudi Arabia.
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Raheel, M., Inc, M., Tala-Tebue, E. et al. Breather, kink and rogue wave solutions of Sharma-Tasso-Olver-like equation. Opt Quant Electron 54, 560 (2022). https://doi.org/10.1007/s11082-022-03933-z
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DOI: https://doi.org/10.1007/s11082-022-03933-z
Keywords
- STOLE
- Hirota bilinear method
- Breather-wave
- Kink solitary and rogue wave
- One-, two- and three-wave solutions