Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM

Öz

In this study, we have worked on GKM in order to obtain the soliton solutions of the generalized third-order nonlinear Schrödinger equation. Thus, we have acquired some new soliton solutions of the generalized third-order nonlinear Schrödinger equation which has an important usage area in optical fiber. Also, we have drawn some 2D and 3D surfaces of these obtained results by using Wolfram Mathematica 12. Then, we have shown the validity of the obtained solutions.

Anahtar Kelimeler

• Generalized Kudryashov method
• generalized third-order nonlinear Schrödinger equation
• soliton solutions

Kaynakça

1. Arshad M, Seadawy AR, Lu D, 2017a. Bright–dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its application in optics. Journal of Electromagnetic Waves and Applications, 31(16): 1711–1721.
2. Arshad M, Seadawy AR, Lu D, 2017b. Exact bright–dark solitary wave solutions of the higher-order cubic–quintic nonlinear Schrödinger equation and its stability. Optik-International Journal for Light and Electron Optics, 138: 40-49.
3. Azzouzi F, Triki H, Mezghiche K, El Akrmi A, 2009. Solitary wave solutions for high dispersive cubic–quintic nonlinear Schrödinger equation. Chaos Solitons and Fractals, 39(3): 1304-1307.
4. Biswas A, Triki H, Zhou Q, Moshokoa SP, Ullah MZ, Belic M, 2017. Cubic–quartic optical solitons in Kerr and power law media. Optik-International Journal for Light and Electron Optics, 144: 357–362.
5. Chettouh S, Triki H, El-Akrmi Zhou AQ, Moshokoa SP, Ullah MZ, Biswas A, Belic M, 2017. Dipole solitons in an extended nonlinear Schrödinger's equation with higher-order even and odd terms. Optik-International Journal for Light and Electron Optics, 145: 644-649.
6. Chowdury A, Kedziora DJ, Ankiewicz A, Akhmediev N, 2014. Soliton solutions of an integrable nonlinear Schrodinger equation with quintic terms. Physical Review, 90(032922): 1-9.
7. Hosseini K, Osman MS, Mirzazadeh M, Rabiei F, 2020. Investigation of different wave structures to the generalized third-order nonlinear Scrödinger equation. Optik-International Journal for Light and Electron Optics, 206(164259): 1-7.
8. Liu W, Qiu DQ, He JS, 2015. Localized properties of rogue wave for a higher-order nonlinear Schrödinger equation. Communications in Theoretical Physics, 63(5): 525-534.

9. Lu D, Seadawy AR, Wang J, Arshad M, Farooq U, 2019. Soliton solutions of the generalised third-order nonlinear Schrödinger equation by two mathematical methods and their stability. Pramana Journal of Physics, 93(44): 1-9.
10. Ma YL, 2019. Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in optical fibers. Nonlinear Dynamics, 97(1): 95-105.
11. Nasreen N, Seadawy AR, Lu D, Albarakati WA, 2019. Dispersive solitary wave and soliton solutions of the gernalized third order nonlinear Schrödinger dynamical equation by modified analytical method. Results in Physics, 15(102641): 1-7.
12. Pandir Y, Tuluce Demiray S, Bulut H, 2016. A new approach for some NLDEs with variable coefficients. Optik-International Journal for Light and Electron Optics, 127(23): 11183-11190.
13. Seadawy AR, Kumar D, Chakrabarty AK, 2018. Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method. European Physical Journal Plus, 133(182): 1-11.
14. Seadawy AR, Arshad M, Lu D, 2020a. The weakly nonlinear wave propagation of the generalized third-order nonlinear Schrödinger equation and its applications. Waves in Random and Complex Media, 1-13.
15. Seadawy AR, Nasreen N, Lu D, 2020b. Complex model ultra-short pulses in optical fibers via generalized third-order nonlinear Schrödinger dynamical equation. International Journal of Modern Physics B, 34(17): 1-9.
16. Triki H, Taha TR, 2012. Solitary wave solutions for a higher order nonlinear Schrödinger equation. Mathematics and Computers in Simulation, 82(7): 1333-1340.
17. Triki H, Choudhuri A, Porsezian K, Dinda PT, 2018. Dark solitons in an extended nonlinear Schrödinger equation with higher-order odd and even terms. Optik-International Journal for Light and Electron Optics, 164: 661-670.
18. Tuluce Demiray S, Bulut H, 2015. New exact solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells equation. Entropy, 17(9): 6025-6043.
19. Tuluce Demiray S, Bulut H, 2016. Generalized Kudryashov method for nonlinear fractional double sinh-poisson equation. Journal of Nonlinear Science and Applications, 9(3): 1349-1355.
20. Tuluce Demiray S, Bulut H, 2017. New soliton solutions of Davey-Stewartson equation with power-law nonlinearity. Optical and Quantum Electronics, 49(117): 1-8.
21. Tuluce Demiray S, Bulut H, 2019. Soliton solutions of some non-linear evolution problems by GKM. Neural Computing and Applications, 31(1): 287-294.
22. Xu LP, Zhang JL, 2007. Exact solutions to two higher order nonlinear Schrodinger equations. Chaos Solitons and Fractals, 31(4): 937-942.