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Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation

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Abstract

In this article, Modified \(1/G^{\prime}\)-expansion and Modified Kudryashov methods are applied to generate traveling wave solutions of Perturbed Chen-Lee-Liu equation. The similar and different aspects of the solutions produced by both analytical methods are discussed. By giving special values to the constants in the solutions obtained by analytical methods, 2D, 3D and contour graphics representing the shape of the standing wave at any time are presented. Additionally, the advantages and disadvantages of the two analytical methods are discussed and presented. Also, a solitary wave is produced by giving special values to the parameters in the hyperbolic type complex traveling wave solution. Simulations are created for different values of the amplitute and velocity propagation parameters of the solitary wave. The values of these parameters are calculated for the breakage event physically. A computer package program is used for operations such as solving complex operations, drawing graphics and solving systems of algebraic equations.

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References

  • Band, Y.B., Trippenbach, M.: Optical wave-packet propagation in nonisotropic media. Phys. Rev. Lett. 76(9), 1457–1460 (1996)

    Article  ADS  Google Scholar 

  • Biswas, A., et al.: Chirped optical solitons of Chen–Lee–Liu equation by extended trial equation scheme. Optik 156, 999–1006 (2018)

    Article  ADS  Google Scholar 

  • Chen, H.H., Lee, Y.C., Liu, C.S.: Integrability of nonlinear Hamiltonian systems by inverse scattering method. Phys. Scr. 20(3–4), 490 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  • Chen, L., Yang, L., Zhang, R., Cui, J.: Generalized (2+1)-dimensional mKdV-Burgers equation and its solution by modified hyperbolic function expansion method. Results Phys. 13, 102280 (2019)

    Article  Google Scholar 

  • Duran, S.: Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics. Int. J. Mod. Phys. B. 2150130 (2021a)

  • Duran, S.: Extractions of travelling wave solutions of (2+1)-dimensional Boiti–Leon–Pempinelli system via (G'/G,1/G)-Expansion Method. Opt. Quantum Electron. 53(6), 1–12 (2021b)

  • Duran, S.: Dynamic interaction of behaviors of time-fractional shallow water wave equation system. Mod. Phys. Lett. B. 2150353 (2021c). https://doi.org/10.1142/s021798492150353X

  • Duran, S.: Solitary wave solutions of the coupled konno-oono equation by using the functional variable method and the two variables (G’/G,1/G)-expansion method. Adıyaman Üniversitesi Fen Bilim. Derg. 10(2), 585–594 (2020)

    Google Scholar 

  • Durur, H.: Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method. Mod. Phys. Lett. B 34(03), 2050036 (2020a)

    Article  ADS  MathSciNet  Google Scholar 

  • Durur, H., Yokuş, A., Kaya D.: Hyperbolic type traveling wave solutions of regularized long wave equation. Bilec. Şeyh Edebali Üniversitesi Fen Bilim. Derg. 7(2) (2020b). https://doi.org/10.35193/bseufbd.698820

  • Durur, H., Ilhan, E., Bulut, H.: Novel complex wave solutions of the (2+1)-dimensional hyperbolic nonlinear schrödinger equation. Fractal Fract. 4(3), 41 (2020c)

    Article  Google Scholar 

  • Gu, Y., Yuan, W., Aminakbari, N., Jiang, Q.: Exact solutions of the Vakhnenko-Parkes equation with complex method. J. Funct. Spaces (2017). https://doi.org/10.1155/2017/6521357

  • Guerrero Sánchez, Y., Sabir, Z., Günerhan, H., Baskonus, H.M.: Analytical and approximate solutions of a novel nervous stomach mathematical model. Discrete Dyn. Nat. Soc. (2020). https://doi.org/10.1155/2020/5063271

  • Hosseini, K., Mirzazadeh, M., Rabiei, F., Baskonus, H.M., Yel, G.: Dark optical solitons to the Biswas-Arshed equation with high order dispersions and absence of the self-phase modulation. Optik 209, 164576 (2020a)

    Article  ADS  Google Scholar 

  • Hosseini, K., Mirzazadeh, M., Gómez-Aguilar, J.F.: Soliton solutions of the Sasa-Satsuma equation in the monomode optical fibers including the beta-derivatives. Optik 224, 165425 (2020b)

    Article  ADS  Google Scholar 

  • Hosseini, K., Sadri, K., Mirzazadeh, M., Chu, Y.M., Ahmadian, A., Pansera, B.A., Salahshour, S.: A high-order nonlinear Schrödinger equation with the weak non-local nonlinearity and its optical solitons. Results Phys. 104035 (2021). https://doi.org/10.1016/j.rinp.2021.104035

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

    Article  ADS  Google Scholar 

  • Kabir, M.M., Khajeh, A., Abdi Aghdam, E., YousefiKoma, A.: Modified Kudryashov method for finding exact solitary wave solutions of higher-order nonlinear equations. Math. Methods Appl. Sci. 34(2), 213–219 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  • Kayum, M.A., Barman, H.K., Akbar, M.A.: Exact soliton solutions to the nano-bioscience and biophysics equations through the modified simple equation method. In: Proceedings of the Sixth International Conference on Mathematics and Computing, pp. 469–482. Springer, Singapore (2021)

  • Kirs, M., Karjust, K., Aziz, I., Õunapuu, E., Tungel, E.: Free vibration analysis of a functionally graded material beam: evaluation of the Haar wavelet method. Proc. Estonian Acad. Sci. 67(1) (2018). https://doi.org/10.3176/proc.2017.4.01

  • Kudryashov, N.A.: Exact soliton solutions of the generalized evolution equation of wave dynamics. J. Appl. Math. Mech. 52(3), 361–365 (1988)

    Article  MathSciNet  Google Scholar 

  • Kudryashov, N.A.: Exact solutions of the generalized Kuramoto-Sivashinsky equation. Phys. Lett. A 147(5–6), 287–291 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  • Kudryashov, N.A.: On types of nonlinear nonintegrable equations with exact solutions. Phys. Lett. A 155(4–5), 269–275 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  • Kudryashov, N.A.: Singular manifold equations and exact solutions for some nonlinear partial differential equations. Phys. Lett. A 182(4–6), 356–362 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  • Kudryashov, N.A.: Nonlinear differential equations with exact solutions expressed via the Weierstrass function. Zeitschrift Für Naturforschung A 59(7–8), 443–454 (2004)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: On traveling wave solutions of the Kundu-Eckhaus equation. Optik 224, 165500 (2020a)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Periodic and solitary waves in optical fiber Bragg gratings with dispersive reflectivity. Chin. J. Phys. 66, 401–405 (2020b)

    Article  MathSciNet  Google Scholar 

  • Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik 206, 163550 (2020c)

    Article  ADS  Google Scholar 

  • Kumar, D., Paul, G.C., Biswas, T., Seadawy, A.R., Baowali, R., Kamal, M., Rezazadeh, H.: Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation. Phys. Scr. 96(2), 025218 (2020)

    Article  ADS  Google Scholar 

  • Modanli, M.: On the numerical solution for third order fractional partial differential equation by difference scheme method. Int. J. Optim. Control: Theor. Appl. (IJOCTA) 9(3), 1–5 (2019)

    MathSciNet  Google Scholar 

  • Pervaiz, N., Aziz, I.: Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations. Phys. a: Stat. Mech. Appl. 545, 12 (2020)

    Article  MathSciNet  Google Scholar 

  • Rehman, S.U., Yusuf, A., Bilal, M., Younas, U., Younis, M., Sulaiman, T.A.: Application of (G’/G^2)-expansion method to microstructured solids, magneto-electro-elastic circular rod and (2+1)dimensional nonlinear electrical lines. J. MESA 11(4), 789–803 (2020)

    Google Scholar 

  • Rezazadeh, H., Odabasi, M., Tariq, K. U., Abazari, R., Baskonus, H.M.: On the conformable nonlinear Schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients. Chin. J. Phys. (2021). https://doi.org/10.1016/j.cjph.2021.01.012

  • Seadawy, A.R., Lu, D., Khater, M.M.: Bifurcations of traveling wave solutions for Dodd–Bullough–Mikhailov equation and coupled Higgs equation and their applications. Chin. J. Phys. 55(4), 1310–1318 (2017)

    Article  Google Scholar 

  • Triki, H., Babatin, M.M., Biswas, A.: Chirped bright solitons for Chen–Lee–Liu equation in optical fibers and PCF. Optik 149, 300–303 (2017)

    Article  ADS  Google Scholar 

  • Triki, H., et al.: Chirped w-shaped optical solitons of Chen–Lee–Liu equation. Optik 155, 208–212 (2018a)

    Article  ADS  Google Scholar 

  • Triki, H., et al.: Chirped dark and gray solitons for Chen–Lee–Liu equation in optical fibers and PCF. Optik 155, 329–333 (2018b)

    Article  ADS  Google Scholar 

  • Vahidi, J., Zabihi, A., Rezazadeh, H., Ansari, R.: New extended direct algebraic method for the resonant nonlinear Schrödinger equation with Kerr law nonlinearity. Optik 165936 (2020). https://doi.org/10.1016/j.ijleo.2020.165936

  • Yavuz, M., Ozdemir, N.: An integral transform solution for fractional advection-diffusion problem. Math. Stud. Appl. 2018 4–6, 442 (2018). https://acikerisim.bartin.edu.tr/bitstream/handle/11772/1364/icmsa2018ExtendedBook.pdf?sequence=1#page=450. Accessed 26 January 2021

  • Yavuz, M., Sene, N.: Approximate solutions of the model describing fluid flow using generalized ρ-laplace transform method and heat balance integral method. Axioms 9(4), 123 (2020)

    Article  Google Scholar 

  • Yavuz, M., Yokus, A.: Analytical and numerical approaches to nerve impulse model of fractional-order. Numer. Methods Partial Differ. Equ. 36(6), 1348–1368 (2020)

    Article  MathSciNet  Google Scholar 

  • Yıldırım, Y., et al.: Optical soliton perturbation with Chen–Lee–Liu equation. Optik 220, 165177 (2020)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Yokus, A.: Solutions of some nonlinear partial differential equations and comparison of their solutions, Ph. Diss., Fırat University (2011). https://acikerisim.firat.edu.tr/xmlui/bitstream/handle/11508/20584/292725.pdf?sequence=1;isAllowed=y. Accessed 25 January 2021

  • Yokus, A., Kuzu, B., Demiroğlu, U.: Investigation of solitary wave solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation. Int. J. Mod. Phys. B 33(29), 1950350 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  • Yokuş, A., Kaya, D.: Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics. Int. J. Mod. Phys. B, 2050282 (2020). https://doi.org/10.1142/S0217979220502823

  • Yokuş, A., Durur, H., Abro, K.A., Kaya, D.: Role of Gilson-Pickering equation for the different types of soliton solutions: a nonlinear analysis. Eur. Phys. J. plus 135(8), 1–19 (2020)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Firat University, 23100, Elazig, Turkey

    Asıf Yokuş

  2. Department of Computer Engineering, Faculty of Engineering, Ardahan University, 75000, Ardahan, Turkey

    Hülya Durur

  3. Department of Mathematics and Science Education, Faculty of Education, Adıyaman University, 02040, Adıyaman, Turkey

    Serbay Duran

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  1. Asıf Yokuş
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  2. Hülya Durur
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Correspondence to Hülya Durur.

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Yokuş, A., Durur, H. & Duran, S. Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation. Opt Quant Electron 53, 402 (2021). https://doi.org/10.1007/s11082-021-03036-1

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