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Non-linear soliton solutions of perturbed Chen-Lee-Liu model by \(\Phi ^{6}-\)model expansion approach

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Abstract

This study deals with the perturbed Chen-Lee-Liu governing mode which portrays the propagating phenomena of the optical pulses in the discipline of optical fiber and plasma. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we use an analytical approach to find traveling wave solutions. One of the generalized techniques \(\Phi ^{6}-\)model expansion method is exerted to find new solitary wave profiles. It is an effective, and reliable technique that provides generalized solitonic wave profiles including numerous types of soliton families. As a result, solitonic wave patterns attain, like Jacobi elliptic function, periodic, dark, bright, singular, dark-bright, exponential, trigonometric, and rational solitonic structures, etc. The constraint corresponding to each obtained solution provides the guarantee of the existence of the solitary wave solutions. The graphical 2-D, 3-D, and contour visualization of the obtained results is presented to express the pulse propagation behaviors by assuming the appropriate values of the involved parameters. The \(\Phi ^{6}-\)model expansion method is simple which can be easily applied to other complex non-linear models and get solitary wave structures.

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References

  • Abdul Kayum, M., Ali Akbar, M., Osman, M.S.: Stable soliton solutions to the shallow water waves and ion-acoustic waves in a plasma. Waves Random Complex Media (2020). https://doi.org/10.1080/17455030.2020.1831711

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Abdulkadir Sulaiman, T., Yusuf, A.: Dynamics of lump-periodic and breather waves solutions with variable coefficients in liquid with gas bubbles. Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2021.1897708

  • Adel, M., Baleanu, D., Sadiya, U., Arefin, M.S., Uddin, M.H., Elamin, M.N., Osman, M.S.: Inelastic soliton wave solutions with different geometrical structures to fractional order nonlinear evolution equations. Results Phys. 38, 105661 (2022)

  • Akinyemi, L., Inc, M., Khater, M.M.A., Rezazadeh, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt. Quant. Electron. 54, 191 (2022)

  • Aktar, M.S., Akbar, M.A., Osman, S.: Spatio-temporal dynamic solitary wave solutions and diffusion effects to the nonlinear diffusive predator-prey system and the diffusion-reaction equations. Chaos Solitons Fract. 160, 112212 (2022)

  • Ali, K.K., Wazwaz, A.M., Osman, M.S.: Optical soliton solutions to the generalized nonautonomous nonlinear Schrödinger equations in optical fibers via the sine-Gordon expansion method. Optik 208, 164132 (2020)

  • Ali, K.K., Yilmazer, R., Yokus, A., Bulut, H.: Analytical solutions for the (3+1)-dimensional nonlinear extended quantum Zakharov-Kuznetsov equation in plasma physics. Phys. A Stat. Mech. Appl. 548, 124327 (2020)

  • Ali, K.K., Yilmazer, R., Osman, M.S.: Dynamic behavior of the (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schif equation. Opt. Quant. Electron. 54, 160 (2022)

  • Baskonus, H.M., Sulaiman, T.A., Bulut, H.: On the exact solitary wave solutions to the long-short wave interaction system. In: ITM web of conferences, vol. 22, pp. 01063. EDP Sciences (2018)

  • Bazighifan, O.: An approach for studying asymptotic properties of solutions of neutral differential equations. Symmetry 12(4), 555 (2020)

  • Bazighifan, O., Kuman, P.: Oscillation theorems for advanced differential equations with p-laplacian like operators. Mathematics 8(5), 821 (2020)

  • Bazighifan, O., Alotaibi, H., Mousa, A.A.A.: Neutral delay differential equations: oscillation conditions for the solutions. Symmetry 13(1), 101 (2021a)

  • Bazighifan, O., Abdeljawad, T., Al-Mdallal, Q.M.: Differential equations of even-order with p-Laplacian like operators: qualitative properties of the solutions. Adv. Diff. Eq. 2021, 96 (2021b)

  • Bibi, K.: The \(\Phi 6-\)model expansion method for solving the Radhakrishnan-Kundu-Lakshmanan equation with Kerr law nonlinearity. Optik 234, 166614 (2021)

  • Biswas, A.: Chirp-free bright optical soliton perturbation with Chen-Lee-Liu equation by traveling wave hypothesis and semi-inverse variational principle. Optik 172, 772–776 (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)

  • 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)

  • Fahim, M.R.A., Kundu, P.R., Islam, M.E., Akbar, M.A., Osman, M.S.: Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach. J. Ocean Eng. Sci. (2021). https://doi.org/10.1016/j.joes.2021.08.009

  • Gao, W., Ismael, H.F., Bulut, H., Baskonus, H.M.: Instability modulation for the (2+ 1)- dimension paraxial wave equation and its new optical soliton solutions in Kerr media. Phys. Scr. 95(3), 035207 (2020a)

  • Gao, W., Ismael, H.F., Husien, A.M., Bulut, H., Baskonus, H.M.: Optical soliton solutions of the cubicquartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation with the parabolic law. Appl. Sci. 10(1), 219 (2020b)

  • Ghanbari, B., Osman, M.S., Baleanu, D.: Generalized exponential rational function method for extended Zakharov-Kuzetsov equation with conformable derivative. Mod. Phys. Lett. A V34(20), 1950155 (2019)

  • Ghanbari, B., Kumar, S., Niwas, M., Baleanu, D.: The Lie symmetry analysis and exact Jacobi elliptic solutions for the Kawahara-KdV type equations. Results Phys. 23, 104006 (2021)

  • Inan, I.E., Inc, M., Rezazadeh, H., Akinyemi, L.: Optical solitons of \((3+1)\) dimensional and coupled nonlinear Schrodinger equations. Opt. Quant. Electron. 54, 246 (2022)

  • Ismael, H.F., Bulut, H., Baskonus, H.M.: Optical soliton solutions to the Fokas-Lenells equation via sine- Gordon expansion method and \((m + \frac{G^{\prime }}{G})-\)expansion method. Pramana 94(1), 35 (2020)

  • Ismael, H.F., Okumus, I., Akturk, T., Bulut, H., Osman, M.S.: Analyzing study for the 3D potential Yu-Toda-Sasa-Fukuyama equation in the two-layer liquid medium. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.03.017

    Article  Google Scholar 

  • Karaman, B.: The use of improved-F expansion method for the time-fractional Benjamin-Ono equation. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie. A Math. 115(3), 1–7 (2021)

    MathSciNet  Google Scholar 

  • Khater, M., Jhangeer, A., Rezazadeh, H., Akinyemi, L., Akbar, M.A., Inc, M., Ahmad, H.: New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques. Opt. Quant. Electron 53(11), 609 (2021)

  • Khater, M.M.A., Jhangeer, A., Rezazadeh, H., Akinyemi, L., Akbar, M.A., Inc, M., Ahmad, H.: New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques. Opt. Quant. Electron. 53, 609 (2021)

  • 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 Schröinger equation. Opt. Quant. Electron 53, 702 (2021)

  • Khodadad, F.S., Mirhosseini-Alizamini, S.M., Günay, B., Akinyemi, L., Rezazadeh, H.: Inc: Abundant optical solitons to the Sasa-Satsuma higher-order nonlinear Schrödinger equation. Opt. Quant. Electron. 53, 702 (2021)

  • Kudryashov, N.A.: General solution of the traveling wave reduction for the perturbed Chen-Lee-Liu equation. Optik 186, 339–349 (2019)

    Article  ADS  Google Scholar 

  • Kumar, S., Dhiman, S.K., Baleanu, D., Osman, M.S., Wazwaz, A.M.: Lie symmetries, closed-form solutions, and various dynamical profiles of solitons for the variable coefficient (2+1)-dimensional KP equations. Symmetry 14(3), 597 (2022)

  • Lü, D.: Jacobi elliptic function solutions for two variant Boussinesq equations. Chaos Solitons Fractals 24(5), 1373–1385 (2005)

  • Moaaz, O., El-Nabulsi, R.A., Bazighifan, O.: Oscillatory behavior of fourth-order differential equations with neutral delay. Symmetry 12(3), 371 (2020)

  • Osman, S.: One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada-Kotera equation. Nonlinear Dyn. 96, 1491–1496 (2019)

  • 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)

  • Raheel, M., Inc, M., Tebue, E.T., Bayram, M.: Optical solitons of the Kudryashov equation via an analytical technique. Opt. Quant. Electron. 54, 340 (2022)

  • Rehman, S.U., Yusuf, A., Bilal, M., Younas, U., Younis, M., Sulaiman, T.A.: Application of \((\frac{G^{\prime }}{G^{2}})\)-expansion method to microstructured solids, magneto-electro-elastic circular rod and (2+ 1)-dimensional nonlinear electrical lines. Math. Eng. Sci. Aerosp. 11(4), 789–803 (2020)

  • Rezazadeh, H., Osman, M.S., Eslami, M., Ekici, M., Sonmezoglu, A., Asma, M., Othman, W.A.M., Wong, B.R., Mirzazadeh, M., Zhou, Q., Biswas, A., Jbelic, M.: Mitigating Internet bottleneck with fractional temporal evolution of optical solitons having quadratic-cubic nonlinearity. Optik 164, 84–92 (2018)

  • Santra, S.S., Ghosh, T., Bazighifan, O.: Explicit criteria for the oscillation of second-order differential equations with several sub-linear neutral coefficients. Adv. Diff. Eq. 2020, 643 (2020)

  • Srivastava, H.M., Baleanu, D., Machado, J.A.T., Osman, M.S., Rezazadeh, H., Arshed, S., Günerhan, H.: Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method. Phys. Scr. 95(7), 075217 (2020)

  • Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: The dynamic behaviors of the Radhakrishnan-Kundu-Lakshmanan equation by Jacobi elliptic function expansion technique. Opt. Quant. Electron. 54, 292 (2022)

  • Tarla, S., Karmina, K.A., Yilmazer, R., Osman, M.S.: New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method. Opt. Quan. Elec. 54, 131 (2022)

  • Yildirim, Y.: Optical solitons with Biswas-Arshed equation by F-expansion method. Optik 227, 165788 (2021)

  • Yildirim, Y., Biswas, A., Asma, M., Ekici, M., Ntsime, B.P., Zayed, E.M., Moshokoa, S.P., Alzahrani, A.K., Belic, M.R.: Optical soliton perturbation with Chen-Lee-Liu equation. Optik 220, 165177 (2020)

  • Zafar, A., Shakeel, M., Ali, A., Akinyemi, L., Rezazadeh, H.: Optical solitons of nonlinear complex Ginzburg- Landau equation via two modified expansion schemes. Optic Quantum Electron 54(1), 5 (2022)

  • Zafar, A., Inc, M., Shakoor, F., Ishaq, M.: Investigation for soliton solutions with some coupled equations. Opt. Quant. Electron. 54, 243 (2022)

  • Zayed, E.M.E., Shohib, R.M.A.: Solitons and other solutions for two higher-order nonlinear wave equations of KdV type using the unified auxiliary equation method. Acta Phys. Pol. A 136(1), 33–41 (2019)

  • Zayed, E.M., Gepreel, K.A., Shohib, R.M., Alngar, M.E., Yildirim, Y.: Optical solitons for the perturbed Biswas-Milovic equation with Kudryashov’s law of refractive index by the unified auxiliary equation method. Optik 230, 166286 (2021)

  • Zhang, R.F., Bilige, S.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation. Nonlinear Dyn. 95(4), 3041–3048 (2019)

  • Zhang, R.F., Li, M.C., Yin, H.M.: Rogue wave solutions and the bright and dark solitons of the (3+ 1)-dimensional Jimbo-Miwa equation. Nonlinear Dyn. 103(1), 1071–1079 (2021)

  • Zhang, R., Bilige, S., Chaolu, T.: Fractal solitons, arbitrary function solutions, exact periodic wave and breathers for a nonlinear partial differential equation by using bilinear neural network method. J. Syst. Sci. Complex. 34(1), 122–139 (2021)

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Acknowledgements

Waqas Ali Faridi and Muhammad Imran Asjad are greatly obliged and thankful to the University of Management and Technology Lahore, Pakistan for facilitating and supporting the research work.

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Waqas Ali Faridi & Muhammad Imran Asjad

  2. Department of Mathematics, Cankaya University, 06790, Ankara, Turkey

    Fahd Jarad

  3. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Fahd Jarad

  4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Fahd Jarad

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  1. Waqas Ali Faridi
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  2. Muhammad Imran Asjad
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  3. Fahd Jarad
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Faridi, W.A., Asjad, M.I. & Jarad, F. Non-linear soliton solutions of perturbed Chen-Lee-Liu model by \(\Phi ^{6}-\)model expansion approach. Opt Quant Electron 54, 664 (2022). https://doi.org/10.1007/s11082-022-04077-w

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