Abstract
In this work, a variety of optical soliton solutions are derived for a nonlinear generalized equation with variable coefficients. At first, a computational approach is used to obtain solutions for the proposed model for a particular case. After, a generalized approach is considered to obtain other type of solutions given in a more general form. From the model considered here, the classical perturbed Fokas-Lenells equation is obtained and new optical soliton solutions for this last case are presented. Finally, some conclusions are given.
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Akinyemi, L.: Two improved techniques for the perturbed nonlinear Biswas-Milovic equation and its optical solitons. Optik 243, 167477 (2021)
Akinyemi, L., Senol, M., Iyiola, O.S.: Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method. Math. Comput. Simul. 182, 211–233 (2021)
Akinyemi, L., Senol, M., Mirzazadeh, M., Eslami, M.: Optical solitons for weakly nonlocal Schrödinger equation with parabolic law nonlinearity and external potential. Optik 230, 166281 (2021)
Al-Ghafri, K.S., Krishnan, E.V., Biswas, A.: Chirped optical soliton perturbation of Fokas-Lenells equation with full nonlinearity. Adv. Differ. Equ. 2020(1), 1–12 (2020)
Bansal, A., Kara, A.H., Biswas, A., Moshokoa, S.P., Belic, M.: Optical soliton perturbation, group invariants and conservation laws of perturbed Fokas-Lenells equation. Chaos Solitons Fractals 114, 275–280 (2018)
Biswas, A., Ekici, M., Sonmezoglu, A., Alshomrani, A.S., Zhou, Q., Moshokoa, S.P., Belic, M.: Chirped optical solitons of Chen-Lee-Liu equation by extended trial equation scheme. Optik 156, 999–1006 (2018)
Chen, Y.Q., Tang, Y.H., Manafian, J., Rezazadeh, H., Osman, M.S.: Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model. Nonlinear Dyn. 105, 2539–2548 (2021)
Dhiman, S.K., Kumar, S., Kharbanda, H.: An extended (3+ 1)-dimensional Jimbo-Miwa equation: Symmetry reductions, invariant solutions and dynamics of different solitary waves. Modern Phys. Lett. B 35(34), 2150528 (2021)
Ghanbari, B.: Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative. Math. Methods Appl. Sci. 44(11), 8759–8774 (2021)
Ghanbari, B.: On novel nondifferentiable exact solutions to local fractional Gardner’s equation using an effective technique. Math. Methods Appl. Sci. 44(6), 4673–4685 (2021)
Ghanbari, B., Nisar, K.S., Aldhaifallah, M.: Abundant solitary wave solutions to an extended nonlinear Schrödingers equation with conformable derivative using an efficient integration method. Adv. Differ. Equ. 2020(1), 1–25 (2020)
Gomez, C.A., Jhangeer, A., Rezazadeh, H., Talarposhti, R., Bekir, A.: Closed form solutions of the perturbed Gerdjikov-Ivanov equation with variable coefficients. East Asian J. Appl. Math. 11(1), 207–218 (2021)
Gómez, S., Cesar, A.: Exact solutions for a generalized Higgs equation. J. King Saud Univ.-Sci. 32(1), 48–53 (2020)
Gómez, S.C.A., Salas, A.H.: The Cole-Hopf transformation and improved tanh-coth method applied to new integrable system (KdV6). Appl. Math. Comput. 204(2), 957–962 (2008)
Hafez, M.G., Alam, M.N., Akbar, M.A.: Traveling wave solutions for some important coupled nonlinear physical models via the coupled Higgs equation and the Maccari system. J. King Saud Univ.-Sci. 27(2), 105–112 (2015)
Hajiseyedazizi, S.N., Samei, M.E., Alzabut, J., Chu, Y.M.: On multi-step methods for singular fractional q-integro-differential equations. Open Math. 19(1), 1378–1405 (2021)
Hasheimi, M.S., Baleanu, D.: Lie Symmetry Analysis of Fractional Differential Equations. CRC Press, London (2020)
Hashemi, M.S.: Some new exact solutions of (2+ 1)-dimensional nonlinear Heisenberg ferromagnetic spin chain with the conformable time fractional derivative. Opt. Quant. Electron. 50(2), 1–11 (2018)
He, Z.Y., Abbes, A., Jahanshahi, H., Alotaibi, N.D., Wang, Y.: Fractional-order discrete-time SIR epidemic model with vaccination: chaos and complexity. Mathematics 10(2), 165 (2022)
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(1), 4 (2021)
Jin, F., Qian, Z.S., Chu, Y.M., ur Rahman, M.: On nonlinear evolution model for drinking behavior under Caputo-Fabrizio derivative. J. Appl. Anal. Comput. 12(2), 790–806 (2022)
Kaur, L., Wazwaz, A.M.: Optical solitons for perturbed Gerdjikov-Ivanov equation. Optik 174, 447–451 (2018)
Khodadad, F.S., Mirhosseini-Alizamini, S.M., Günay, B., Akinyemi, L., Rezazadeh, H., Inc, M.: Abundant optical solitons to the Sasa-Satsuma higher-order nonlinear Schrödinger equation. Opt. Quant. Electron. 53(12), 1–17 (2021)
Kudryashov, N.A.: One method for finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 17(6), 2248–2253 (2012)
Kumar, S.: Some new families of exact solitary wave solutions of the Klein-Gordon-Zakharov equations in plasma physics. Pramana 95(4), 1–15 (2021)
Kumar, S., Rani, S.: Invariance analysis, optimal system, closed-form solutions and dynamical wave structures of a (2+ 1)-dimensional dissipative long wave system. Phys. Scr. 96(12), 125202 (2021)
Miura, R..M.: Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation. J. Math. Phys. 9(8), 1202–1204 (1968)
Nirmala, N., Vedan, M.J., Baby, B.V.: Auto-Bäcklund transformation, Lax pairs, and Painlevé property of a variable coefficient Korteweg-de Vries equation. Int. J. Math. Phys. 27(11), 2640–2643 (1986)
Rashid, S., Abouelmagd, E.I., Khalid, A., Farooq, F.B., Chu, Y.M.: Some recent developments on dynamical h-discrete fractional type inequalities in the frame of nonsingular and nonlocal kernel. Fractals 30(2), 2240110 (2022)
Salas, A.: Special symmetries to standard Riccati equations and applications. Appl. Math. Comput. 216(10), 3089–3096 (2010)
Salas, A.H., Gómez, S.C.A.: Exact solutions for a third-order KdV equation with variable coefficients and forcing term. Math. Probl. Eng. 1, 1 (2009). https://doi.org/10.1155/2009/737928
Srivastava, M.H., Günerhan, H., Ghanbari, B.: Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity. Math. Methods Appl. Sci. 42(18), 7210–7221 (2019)
Wang, F., Khan, M.N., Ahmad, I., Ahmad, H., Abu-Zinadah, H., Chu, Y.M.: Numerical solution of traveling waves in chemical kinetics: time-fractional fishers equations. Fractals 30(02), 2240051 (2022)
Wazwaz, A.M.: The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl. Math. Comput. 188(2), 1467–1475 (2007)
Yang, L.C.: The applications of bifurvation method to a higher-order KdV equation. Math. Anal. Appl. 275, 1–12 (2012)
Yıldırım, Y.: Optical soliton molecules of Manakov model by modified simple equation technique. Optik 185, 1182–1188 (2019)
Zafar, A., Shakeel, M., Ali, A., Akinyemi, L., Rezazadeh, H.: Optical solitons of nonlinear complex Ginzburg-Landau equation via two modified expansion schemes. Opt. Quant. Electron. 54(1), 1–15 (2022)
Zayed, E.M.E., Alurrfi, K.A.E.: New extended auxiliary equation method and its applications to nonlinear Schrödinger-type equations. Optik 127(20), 9131–9151 (2016)
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Gomez S, C., Roshid, HO., Inc, M. et al. On soliton solutions for perturbed Fokas–Lenells equation. Opt Quant Electron 54, 370 (2022). https://doi.org/10.1007/s11082-022-03796-4
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DOI: https://doi.org/10.1007/s11082-022-03796-4