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Optical and Quantum Electronics

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01.03.2023

On solitary wave solutions for the extended nonlinear Schrödinger equation via the modified F-expansion method

verfasst von: Muslum Ozisik, Aydin Secer, Mustafa Bayram

Erschienen in: Optical and Quantum Electronics | Ausgabe 3/2023

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Abstract

Because the importance of the optical wave propagation in fibers, we seek for the optical travelling wave solutions and effect of the third-order dispersion parameter for the extended nonlinear Schrödinger equation (NLSE) which is used to describe the femtosecond(fs) pulse propagation in optical fiber. We have used the modified F-expansion method because it is effective, sufficient and offers more solutions for this kind of problems. First, we obtain the nonlinear ordinary differential form (NODE) by using the wave transformation on the investigated extended nonlinear Schrödinger equation. Then, we propose the modified F-expansion method to get solution of the equation as the NODE form, and by calculating the balancing constant over the NODE form. By substituting the proposed solution function and its derivatives in the NODE form, we obtain an algebraic equation system over this NODE. With the solution of this system, we obtain the appropriate solution sets for the undefined parameters, and then, using the appropriate sets, the proposed solution function, the F-expansion solution functions, and the wave transform, together, we obtain the solution functions of the investigated problem. In order to contribute to the physical interpretation of the problem, 3D, 2D and contour graphs of the obtained solution functions were plotted and interpreted. The problem has not been examined by considering two different situations with the effect of third order dispersion parameter as in this study, before. In this respect, the results obtained in the study are new, and it is believed that they will contribute to the studies in this field.

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Ali, K., Rizvi, S.T.R., Ahmad, S., Bashir, S., Younis, M.: Bell and kink type soliton solutions in birefringent nano-fibers. Optik 142, 327–333 (2017)ADS

Arnous, A.H., Ullah, M.Z., Asma, M., Moshokoa, S.P., Zhou, Q., Mirzazadeh, M., Biswas, A.: Dark and singular dispersive optical solitons of Schrödinger–Hirota equation by modified simple equation method. Optik 136, 445–450 (2017)ADS

Arshed, S., Biswas, A., Zhou, Q., Khan, S., Adesanya, S., Moshokoa, S.P., Belic, M.: Optical solitons pertutabation with Fokas-Lenells equation by exp(-\(\phi\)(\(\xi\)))-expansion method. Optik 179, 341–345 (2019)ADS

Arshed, S., Biswas, A., Guggilla, P., Alshomrani, A.S.: Optical solitons for Radhakrishnan–Kundu–Lakshmanan equation with full nonlinearity. Phys. Lett. A 384(26), 126191 (2020)MathSciNetMATH

Aslan, E.C., Tchier, F., Inc, M.: On optical solitons of the Schrödinger–Hirota equation with power law nonlinearity in optical fibers. Superlattices Microstruct. 105, 48–55 (2017)ADS

Baskonus, H.M., Sulaiman, T.A., Bulut, H.: Dark, bright and other optical solitons to the decoupled nonlinear Schrödinger equation arising in dual-core optical fibers. Opt. Quant. Electron. 50(4), 1–2 (2018a)

Baskonus, H.M., Sulaiman, T.A., Bulut, H.: Bright, dark optical and other solitons to the generalized higher-order NLSE in optical fibers. Opt. Quant. Electron. 50(6), 1–2 (2018b)

Biswas, A., Ekici, M., Sonmezoglu, A., Triki, H., Alshomrani, A.S., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical solitons for Gerdjikov–Ivanov model by extended trial equation scheme. Optik 157, 1241–1248 (2018)ADS

Borich, M.A., Smagin, V.V., Tankeev, A.P.: Stationary states of extended nonlinear Schrodinger equation with a source. Phys. Met. Metall. 103(2), 118–130 (2007)

Cheng-Lin, B., Hong, Z., Wei-Tao, W.: Exact solutions to extended nonlinear Schrödinger equation in monomode optical fiber. Commun. Theor. Phys. 45(1), 131–134 (2006)ADSMATH

Chu, Y.-M., Shallal, M.A., Mirhosseini-Alizamini, S.M., Rezazadeh, H., Javeed, S., Baleanu, D.: Application of modified extended tanh technique for solving complex Ginzburg–Landau equation considering Kerr law nonlinearity. Comput. Mater. Continu. 66(2), 1369–1378 (2021)

Crabb, M., Akhmediev, N.: Two-breather solutions for the class i infinitely extended nonlinear Schrodinger equation and their special cases. Nonlinear Dyn. 98(1), 245–255 (2019)MATH

Das, A., Biswas, A., Ekici, M., Zhou, Q., Alshomrani, A.S., Belic, M.R.: Optical solitons with complex Ginzburg-Landau equation for two nonlinear forms using f-expansion. Chin. J. Phys. 61, 255–261 (2019)MathSciNet

Dianchen, L., Seadawy, A.R., Iqbal, M.: Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications. Results Phys. 11, 1161–1171 (2018)ADS

Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas-Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83(1–2), 731–738 (2015)MathSciNetMATH

Frisquet, B., Kibler, B., Fatome, J., Morin, P., Baronio, F., Conforti, M., Millot, G., Wabnitz, S.: Polarization modulation instability in a Manakov fiber system. Phys. Rev. A 92(5), 1 (2015)

Ghanbari, B., Baleanu, D.: New optical solutions of the fractional Gerdjikov–Ivanov equation with conformable derivative. Front. Phys. 8, 1 (2020)

Gordon, J.P.: Theory of the soliton self-frequency shift. Opt. Lett. 11(10), 662 (1986)ADS

He, J., Xu, S., Porsezian, K.: Rogue waves of the Fokas–Lenells equation. J. Phys. Soc. Jpn. 81(4007), 12 (2012)

Houwe, A., Abbagari, S., Betchewe, G., Inc, M., Doka, S.Y., Crépin, K.T., Baleanu, D., Almohsen, B.: Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics. Open Phys. 18(1), 526–534 (2020a)

Houwe, A., Abbagari, S., Salathiel, Y., Inc, M., Doka, S.Y., Crépin, K.T., Baleanu, D.: Complex traveling-wave and solitons solutions to the Klein–Gordon–Zakharov equations. Results Phys. 17, 103127 (2020b)

Huang, Y., Jing, H., Li, M.Y., Zhenjun, Y.Y.: On solutions of an extended nonlocal nonlinear Schrodinger equation in plasmas. Mathematics 8, 7 (2020)

Hussain, A., Jhangeer, A., Abbas, N., Khan, I., Sherif, E.S.M.: Optical solitons of fractional complex Ginzburg–Landau equation with conformable, beta, and m-truncated derivatives: a comparative study. Adv. Differ. Equ. 2020(1), 1 (2020a)

Hussain, A., Jhangeer, A., Tahir, S., Chu, Y.-M., Khan, I., Nisar, K.S.: Dynamical behavior of fractional Chen–Lee–Liu equation in optical fibers with beta derivatives. Results Phys. 18, 111755 (2020b)

Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Dispersive optical solitons and modulation instability analysis of Schrödinger–Hirota equation with spatio-temporal dispersion and Kerr law nonlinearity. Superlattices Microstruct. 113, 319–327 (2018a)

Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Combined optical solitary waves and conservation laws for nonlinear Chen–Lee–Liu equation in optical fibers. Optik 158, 297–304 (2018b)

Iqbal, M., Seadawy, A.: Instability of modulation wave train and disturbance of time period in slightly stable media for unstable nonlinear Schrödinger dynamical equation. Mod. Phys. Lett. B 34, 11 (2020)

Iqbal, M., Seadawy, A.R., Lu, D.: Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods. Mod. Phys. Lett. A 33(32), 1850183 (2018a)

Iqbal, M., Seadawy, A.R., Dianchen, L.: Dispersive solitary wave solutions of nonlinear further modified Korteweg-de vries dynamical equation in an unmagnetized dusty plasma. Mod. Phys. Lett. A 33(37), 1850217 (2018b)

Iqbal, M., Seadawy, A., Dianchen, L.: Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions. Mod. Phys. Lett. B 33, 1950210 (2019)ADSMathSciNet

Iqbal, M., Seadawy, A.R., Khalil, O.H., Dianchen, L.: Propagation of long internal waves in density stratified ocean for the (2+1)-dimensional nonlinear Nizhnik–Novikov–Vesselov dynamical equation. Results Phys. 16, 102838 (2020)

Ismael, H.F., Baskonus, H.M., Bulut, H.: Abundant novel solutions of the conformable Lakshmanan–Porsezian–Daniel model. Discrete Continu. Dyn. Syst. S 14(7), 2311 (2021)MathSciNetMATH

Kara, A.H., Biswas, A., Zhou, Q., Moraru, L., Moshokoa, S.P., Belic, M.: Conservation laws for optical solitons with Chen Lee Liu equation. Optik 174, 195–198 (2018)ADS

Khan, Y.: A novel soliton solutions for the fractal Radhakrishnan–Kundu–Lakshmanan model arising in birefringent fibers. Opt. Quantum Electron. 53(2), 1 (2021)

Kodama, Y., Hasegawa, A.: Nonlinear pulse propagation in a monomode dielectric guide. IEEE J. Quantum Electron. 23(5), 510–524 (1987)ADS

Kudryashov, N.A.: First integrals and general solution of the complex Ginzburg-Landau equation. Appl. Math. Comput. 386, 125407 (2020)MathSciNetMATH

Lou, Yu., Zhang, Y., Ye, R.: Interactional solutions of the extended nonlinear Schrodinger equation with higher-order operators. Int. J. Comput. Math. 99(10), 1989–2000 (2022)MathSciNetMATH

Manafian, J., Lakestani, M.: Optical soliton solutions for the Gerdjikov–Ivanov model via tan(\(\phi\)/2)-expansion method. Optik 127(20), 9603–9620 (2016)ADS

Mitschke, F.M., Mollenauer, L.F.: Discovery of the soliton self-frequency shift. Opt. Lett. 11(10), 659 (1986)ADS

Mohammed, W.W., Ahmad, H., Hamza, A.E., Aly, E.S., ElMorshedy, M., Elabbasy, E.M.: The exact solutions of the stochastic Ginzburg–Landau equation. Results Phys. 23, 103988 (2021)

Monisha, S., Priya, V.N., Senthilvelan, M., Rajasekar, S.: Higher order smooth positron and breather positron solutions of an extended nonlinear Schrodinger equation with the cubic and quartic nonlinearity. Chaos Solitons Fractals 162, 1 (2022)MATH

Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T.A.: Optical soliton solutions to Chen Lee Liu model by the modified extended tanh expansion scheme. Optik 245, 167643 (2021a)

Ozdemir, N., Esen, H., Secer, A., Bayram, M., Sulaiman, T.A., Yusuf, A., Aydin, H.: Optical solitons and other solutions to the Radhakrishnan–Kundu–Lakshmanan equation. Optik 242, 167363 (2021b)

Ramakrishnan, R., Stalin, S., Lakshmanan, M.: Multihumped nondegenerate fundamental bright solitons in n-coupled nonlinear Schrödinger system. J. Phys. A Math. Theor. 54(14), 14LT01 (2021)

Raza, N., Javid, A.: Modulation instability and optical solitons of Radhakrishnan–Kundu–Lakshmanan model. J. Appl. Anal. Comput. 10(4), 1375–1395 (2020)MathSciNetMATH

Rezazadeh, H.: New solitons solutions of the complex Ginzburg–Landau equation with Kerr law nonlinearity. Optik 167, 218–227 (2018)ADS

Rezazadeh, H., Adel, W., Eslami, M., Tariq, K.U., Mirhosseini-Alizamini, S.M., Bekir, A., Chu, Y.-M.: On the optical solutions to nonlinear Schrödinger equation with second-order spatiotemporal dispersion. Open Phys. 19(1), 111–118 (2021)

Savescu, M., Khan, K.R., Kohl, R.W., Moraru, L., Yildirim, A., Biswas, A.: Optical soliton perturbation with improved nonlinear Schrödinger’s equation in nano fibers. J. Nanoelectron. Optoelectron. 8(2), 208–220 (2013)

Seadawy, A.R., Iqbal, M., Dianchen, L.: Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid–gas bubbles under the consideration of heat transfer and viscosity. J. Taibah Univ. Sci. 13(1), 1060–1072 (2019a)

Seadawy, A.R., Iqbal, M., Dianchen, L.: Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width dynamical equation. Comput. Math. Appl. 78(11), 3620–3632 (2019b)

Seadawy, A., Dianchen, L., Iqbal, M.: Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir waves. Pramana 93, 1–10 (2019c)

Seadawy, A.R., Iqbal, M., Dianchen, L.: Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg-de vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma. Physica A 544, 123560 (2020a)

Seadawy, A.R., Iqbal, M., Lu, D.: Propagation of long-wave with dissipation and dispersion in nonlinear media via generalized Kadomtsive–Petviashvili modified equal width-burgers equation. Indian J. Phys. 94(5), 675–687 (2020b)

Seadawy, A.R., Iqbal, M., Dianchen, L.: The nonlinear diffusion reaction dynamical system with quadratic and cubic nonlinearities with analytical investigations. Int. J. Mod. Phys. B 34(09), 2050085 (2020c)

Seadawy, A.R., Iqbal, M., Althobaiti, S., Sayed, S.: Wave propagation for the nonlinear modified Kortewege-de vries Zakharov–Kuznetsov and extended Zakharov–Kuznetsov dynamical equations arising in nonlinear wave media. Opt. Quantum Electron. 53(2), 1 (2021a)

Seadawy, A.R., Nasreen, N., Dian-Chen, L.: Optical soliton and elliptic functions solutions of Sasa–Satsuma dynamical equation and its applications. Appl. Math. A J. Chin. Univ. 36(2), 229–242 (2021b)

Seadawy, A.R., Nasreen, N., Althobaiti, S., Sayed, S., Biswas, A.: Soliton solutions of Sasa–Satsuma nonlinear Schrödinger model and construction of modulation instability analysis. Opt. Quantum Electron. 53(2), 1 (2021c)

Sedletsky, Y.V., Gandzha, I. S.: Hamiltonian form of an extended nonlinear Schrodinger equation for modelling the wave field in a system with quadratic and cubic nonlinearities. In: Mathematical Modelling of Natural Phenomena, vol. 17 (2022)

Singh, H., Kumar, D., Singh, J., Singh, C.: A reliable numerical algorithm for the fractional Klein–Gordon equation. Eng. Trans. 67, 21–34 (2019)

Su, D., Yong, X., Tian, Y., Tian, J.: Breather and rogue wave solutions of an extended nonlinear Schrodinger equation with higher-order odd and even terms. Modern Phys. Lett. B 32(26), 1 (2018)MathSciNet

Sulaiman, T.A., Bulut, H., Atas, S.S.: Optical solitons to the fractional Schrödinger–Hirota equation. Appl. Math. Nonlinear Sci. 4(2), 535–542 (2019)MathSciNet

Sulaiman, T.A., Bulut, H., Baskonus, H.M.: Optical solitons to the fractional perturbed NLSE in nano-fibers. Discrete Continu. Dyn. Syst. 13(3), 925–936 (2020)MathSciNetMATH

Wang, X., Liao, F.: Nontrivial solutions for a nonlinear Schrödinger equation with nonsymmetric coefficients. Nonlinear Anal. 195, 111755 (2020)MathSciNetMATH

Yildirim, Y.: Optical solitons to Sasa–Satsuma model with trial equation approach. Optik 184, 70–74 (2019)ADS

Zakharov, V.E., Schulman, E.I.: To the integrability of the system of two coupled nonlinear Schrödinger equations. Physica D 4(2), 270–274 (1982)ADSMATH

Titel: On solitary wave solutions for the extended nonlinear Schrödinger equation via the modified F-expansion method
verfasst von: Muslum Ozisik
Aydin Secer
Mustafa Bayram
Publikationsdatum: 01.03.2023
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 3/2023
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-022-04476-z

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