Top

Optical and Quantum Electronics

Published in:

01-05-2024

Chirped dark soliton propagation in optical fiber under a self phase modulation and a self-steepening effect for higher order nonlinear Schrödinger equation

Authors: A. Muniyappan, E. Parasuraman, Aly R. Seadawy, J. B. Sudharsan

Published in: Optical and Quantum Electronics | Issue 5/2024

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We have studied the dynamics of various kinds of optical dark solitons like, chirped, chirp-free, M-shaped & wing shaped dark solitons using higher-order nonlinear Schrödinger equation. To obtain the exact analytical solution, we employed mathematical techniques such as the extended rational sinh-cosh and sin-cos methods. Our investigation shows that one can manipulate the shape of both chirp and chirp free dark solitons by properly tuning the magnitude of the self steepening and self phase modulation. The stability of the obtained dark soliton solutions are verified by using linear stability analysis.

previous article Investigation of SPR sensor for immunoglobulin detection by using Ag–-BP on the sensing layer

next article Optical solitons perturbation and traveling wave solutions in magneto-optic waveguides with the generalized stochastic Schrödinger–Hirota equation

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Abdillah Mardi, H., Nasaruddin, N., Ikhwan, M., Nurmaulidar, N., Ramli, M.: Soliton dynamics in optical fiber based on nonlinear Schrödinger equation. Heliyon 9(3), e14235 (2023)

Agrawal, G.P.: ed., Nonlinear Fiber Optics, sixth edition ed. (Academic Press, 2019)

Alka, Amit Goyal, Gupta, Rama, Kumar, C.N., Raju, Thokala Soloman: Chirped femtosecond solitons and double-kink solitons in the cubic-quintic nonlinear Schrödinger equation with self-steepening and self-frequency shift. Phys. Rev. A 84, 063830 (2011)ADS

Aly, R.: Seadawy, Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl. 67, 172–180 (2014)MathSciNet

Aly, R.: Seadawy. Approximation solutions of derivative nonlinear Schrodinger equation with computational applications by variational method. Eur. Phys. J. Plus 130(182), 1–10 (2015)ADS

Aly, R.: Seadawy, Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a magnetized electron-positron plasma, Physica A: Statistical Mechanics and its Applications. Phys. A 455, 44–51 (2016)MathSciNet

Aly, R.: Seadawy, The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrödinger equation and its solutions. Optik 139, 31–43 (2017)

Aly, R.: Seadawy, Muhammad Arshad and Dianchen Lu, The weakly nonlinear wave propagation theory for the Kelvin-Helmholtz instability in magnetohydrodynamics flows. Chaos, Solitons Fractals 139, 110141 (2020)

Arshad, M., Seadawy, A.R., Dianchen, L.: Optical soliton solutions of the generalized higher-order nonlinear Schrödinger equations and their applications. Opt. Quantum Electron. 421, 1–16 (2017)

Boyd, J.P.: Chebyshev and Fourier Spectral Methods, pp. 1–594. Dover Publications Inc., Mineola, New York (2000)

Çelik, Nisa, Seadawy, Aly R.: Yeşim Sağlam Özkan, Emrullah Yaşar, A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws. Chaos, Solitons Fractals 143, 110486 (2021)

Chen, S., Shi, D., Yi, D.: Timing jitter of femtosecond solitons in single-mode optical fibers: A perturbation model. Phys. Rev. E 69, 046602 (2004)ADS

Desaix, M., Helczynski, L., Anderson, D., Lisak, M.: Propagation properties of chirped soliton pulses in optical nonlinear Kerr media. Phys. Rev. E 65, 056602 (2002)ADS

Dianchen, Lu.: Aly Seadawy and M. Arshad, Bright-Dark optical soliton and dispersive elliptic function solutions of Unstable nonlinear Schrodinger equation and its applications, Optical and Quantum Electronics 50(23), 1–10 (2018)

Ding, C.-C., Zhou, Q., Triki, H., Hu, Z.-H.: Opt. Express 30, 40712 (2022)ADS

Du, X.X., Tian, B., Wu, X.Y., Yin, H.M., Zhang, C.R.: Lie group analysis, analytic solutions and conservation laws of the (3+1)-dimensional Zakharov-Kuznetsov-Burgers equation in a collisionless magnetized electron-positron-ion plasma. Eur. Phys. J. Plus 133, 378 (2018)

Eskandar, S., Hoseini, S.M.: Soliton solutions and eigenfunctions of linearized operator for a higher-order nonlinear Schrödinger equation. Chaos, Solitons & Fractals 106, 289–294 (2018)ADSMathSciNet

Feng, W., Chen, L., Ma, G., Zhou, Q.: Nonlinear Dyn. 108, 2483 (2022)

Gao, X.Y.: Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas. Appl. Math. Lett. 91, 165–72 (2019)MathSciNet

Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. John Hopkins University Press, Baltimore, MD (1996)

Goyal, A.A., Gupta, R., Kumar, C.N., Raju, T.S.: Chirped femtosecond solitons and double-kink solitons in the cubicquintic nonlinear Schrödinger equation with self-steepening and self-frequency shift. Phys. Rev. A 84(6), 063810–063817 (2011)

Hamaide, J.P., Emplit, P., Haelterman, M.: Dark-soliton jitter in amplified optical transmission systems. Opt. Lett. 16, 1578–1580 (1991)ADS

Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous Dispersion, Appl. Phys. Lett. 23, 142 (1973)ADS

Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion, Appl. Phys. Lett. 23, 171 (1973)ADS

Iqbal, Mujahid, Seadawy, Aly R., Dianchen, Lu.: Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions. Mod. Phys. Lett. B 33(18), 1950210 (2019)ADSMathSciNet

Jhangeer, Adil, Rezazadeh, Hadi, Seadawy, Aly: A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas-Lenells model, Pramana volume 95, Article number: 41 (2021)

Jinping, T., Guosheng, Z.: Chirped soliton-like solutions for nonlinear Schrödinger equation with variable coefficients. Opt. Commun. 262, 257–262 (2006)

Kartashov, Y.V., Astrakharchik, G.E., Malomed, B.A., Torner, L.: Nature Reviews Physics 1, 185 (2019)ADS

Kavitha, L., Parasuraman, E., Muniyappan, A., Gopi, D., Zdravković, S.: Localized discrete breather modes in neuronal microtubules. Nonlinear Dyn. 88, 2013–2033 (2017)

Kavitha, L., Venkatesh, M., Dhamayanthi, S., Parasuraman, E., Gopi, D.: Optically induced switching of nematic deformations. Phys. Scr. 88, 065015 (2013)ADS

Kavitha, L., Jayanthi, S., Muniyappan, A., Gopi, D.: Protonic transport through solitons in hydrogen-bonded systems. Phys. Scr. 84, 035803 (2011)ADS

Kavitha, L., Muniyappan, A., Zdravković, S., Satarić, M.V., Marlewski, A., Dhamayanthi, S., Gopi, D.: Propagation of kink-antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes. Chin. Phys. B 23, 098703 (2014)ADS

Kengne, E.: Ultrashort optical pulses with nonlinear chirps in non-Kerr media exhibiting higher-order nonlinearities. Opt. Quant. Electron. 55, 1154 (2023)

Khater, A.H., Callebaut, D.K., Malfliet, W., Seadawy, A.R.: Nonlinear dispersive rayleigh-taylor instabilities in magnetohydrodynamic flows. Phys. Scr. 64, 533–547 (2001)ADS

Kivshar, S., Agrawal, G.P.: Optical Solitons: From Fibers to Photonic Crystals. Academic, San Diego (2003)

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

Kruglov, V.I., Peacock, A.C., Harvey, J.D.: Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients. Phys. Rev. Lett. 90, 113902 (2003)ADS

Li, C.: Nonlinear Optics: Principles and Applications (Springer Singapore, 2016)

Liu, S., Fu, Z., Liu, S., Zhao, Q.: Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A 289, 69–74 (2001)ADSMathSciNet

Liu, W.-J., Tian, B., Zhang, H.-Q., Xu, T., Li, H.: Phys. Rev. A 79, 063810 (2009)ADS

Li, Z., Li, L., Tian, H., Zhou, G.: New Types of solitary wave solutions for the higher order nonlinear Schrödinger equation. Phys. Rev. Lett. 84, 4096–4099 (2000)ADS

Li, M., Tian, B., Liu, W.-J., Zhang, H.-Q., Wang, P.: Dark and antidark solitons in the modified nonlinear Schrödinger equation accounting for the self-steepening effect. Phys. Rev. E 81, 046606 (2010)ADS

Malomed, B.A., Mihalache, D.: Rom. J. Phys. 64, 106 (2019)

Mollenauer, L.F., Stolen, R.H., Gordon, J.P.: Experimental observation of picosecond pulse narrowing and solitons in optical fiber. Phys. Rev. Lett. 45, 1095 (1980)ADS

Mollenauer, L.F., Bullough, R.K., Freeman, N.C., Beth, T.: Philosophical transactions of the royal society of London. Ser. A, Math. Phys. Sci. 315, 437 (1985)

Muniyappan, A., Suruthi, A., Monisha, B., Sharon Leela, N., Vijaychales, J.: Dromion-like structures in a cubic-quintic nonlinear Schrödinger equation using analytical methods. Nonlinear Dyn. 104, 1533–1544 (2021)

Muniyappan, A., Athira Priya, O., Amirthani, S., Brintha, K., Biswas, A., Ekici, M., Dakova, A., Alshehri, H.M., Belic, M.R.: Peakon and cuspon excitations in optical fibers for eighth order nonlinear Schrödinger’s model. Optik 243, 167509 (2021)ADS

Muniyappan, A., Sharmila, M., Kaviya Priya, E., et al.: W-shaped chirp free and chirped bright, dark solitons for perturbed nonlinear Schrödinger equation in nonlinear optical fibers. Proc. Est. Acad. Sci. 72, 128–144 (2023)

Muniyappan, A., Monisha, P., Kaviya Priya, E., Nivetha, V.: Generation of wing-shaped dark soliton for perturbed Gerdjikov-Ivanov equation in optical fibre. Optik 230, 166328 (2021)

Muniyappan, A., Sahasraari, L.N., Anitha, S., Ilakiya, S., Biswas, A., Yıldırım, Y., Triki, H., Alshehri, H.M., Belic, M.R.: Family of optical solitons for perturbed Fokas-Lenells equation. Optik 249, 168224 (2022)ADS

Nithyanandan, K., Raja, R.V.J., Porsezian, K., Kalithasan, B.: Phys. Rev. A 86, 023827 (2012)ADS

Petrović, N.Z., Belić, M., Zhong, W.P.: Exact traveling-wave and spatiotemporal solutions to the generalized (2+1)-dimensional Schrodinger equation with polynomial nonlinearity of arbitrary order. Phys. Rev. E 83, 026604 (2011)ADS

Porsezian, K., Nakkeeran, K.: Optical solitons in presence of Kerr dispersion and self-frequency shift. Phys. Rev. Lett. 76, 3955 (1996)ADS

Salin, F., Grangier, P., Roger, G., Brun, A.: Phys. Rev. Lett. 56, 1132 (1986)ADS

Seadawy, A.R., Lu, D.: Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability. Results Phys. 7, 43–48 (2017)ADS

Seadawy, Aly R., Iqbal, Mujahid, Lu, Dianchen.: Application of mathematical methods on the ion sound and Langmuir waves dynamical systems, The Pramana - J. Phys. 93, (10) (2019)

Seadawy, Aly R., Rizvi, Syed T. R., Ali, Ijaz, Younis, Muhammad, Kashif Ali, M.M., Makhlouf, Ali Althobaiti: Conservation laws, optical molecules, modulation instability and Painlevé analysis for the Chen-Lee-Liu model. Opt. Quant. Electron. 53, 172 (2021)

Song, Y., Shi, X., Wu, C., Tang, D., Zhang, H.: Appl. Phys. Rev. 6, 021313 (2019)ADS

Song, Y.F., Guo, J., Zhao, L.M., Shen, D.Y., Tang, D.Y.: Opt. Lett. 39, 3484 (2014)ADS

Sun, M., Deng, S., Chen, D.: The Bäcklund transformation and novel solutions for the Toda lattice. Chaos, Solitons & Fractals 23, 1169–1175 (2005)ADSMathSciNet

Syed, T.R.: Rizvi, Aly R. Seadawy, Sarfaraz Ahmed, Kashif Ali, Einstein’s vacuum field equation: lumps, manifold periodic, generalized breathers, interactions and rogue wave solutions, Optical and Quantum Electronics 55, 181 (2023)

Syed, T.R.: Rizvi, Aly R. Seadawy, Sarfaraz Ahmed, Muhammad Younis, Kashif Ali, Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation, Chaos, Solitons and Fractals 151, 111251 (2021)

Tala-Tebue, E., Seadawy, A.R., Kamdoum-Tamo, P.H., Lu, D.: Dispersive optical soliton solutions of the higher order nonlinear Schrodinger dynamical equation via two diferent methods and its applications. Eur. Phys. J. Plus 133, 289-1-289-10 (2018)

Tang, D., Guo, J., Song, Y., Zhang, H., Zhao, L., Shen, D.: Opt. Express 22, 19831 (2014)ADS

Tao, Y.S., He, J.S.: Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation. Phys. Rev. E 85, 026601 (2012)ADS

Tchepemen, N., Balasubramanian, S., Kanagaraj, N., Kengne, E.: Modulational instability in a coupled nonlocal media with cubic, quintic and septimal nonlinearities. Nonlinear Dyn. 111, 20311–20329 (2023a)

Tchepemen, N., Balasubramanian, S., Chamgoué, A.C., Kengne, E.: Cubic-quintic nonlinear wave patterns and Lagrangian approach to modulational instability in pure-quartic media. Opt. Quant. Electron. 55, 1057 (2023b)

Triki, H., Biswas, A., Milović, D., Belić, M.R.: Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities. Opt. Commun. 366, 362–9 (2016)ADS

Uzunov, I.M., Gerdjikov, V.S.: Self-frequency shift of dark solitons in optical fibers. Phys. Rev. A 47, 1582–1585 (1993)ADS

Vladimir, I., Kruglov, H.: Triki, Propagation of periodic and solitary waves in a highly dispersive cubic-quintic medium with self-frequency shift and self-steepening nonlinearity. Chaos, Solitons & Fractals 164, 112704 (2022)MathSciNet

Wazwaz, A.M.: Higher dimensional nonlinear Schrödinger equations in anomalous dispersion and normal dispersive regimes: Bright and dark optical solitons. Optik 222, 165327 (2020)ADS

Wazwaz, A.M., Kaur, L.: Complex simplified Hirota’s forms and Lie symmetry analysis for multiple real and complex soliton solutions of the modified KdV-Sine-Gordon equation. Nonlinear Dyn. 95, 2209–2215 (2019)

Wazwaz, A.M., Xu, G.Q.: Kadomtsev-Petviashvili hierarchy: two integrable equations with time-dependent coefficients. Nonlinear Dyn. 100, 3711–3716 (2020)

Wenlong, Wang, Li-Chen, Zhao, Charalampidis Efstathios, G., Kevrekidis, P.G.: Dark-dark soliton breathing patterns in multi-component Bose-Einstein condensates. J. Phys. B: At. Mol. Opt. Phys. 54, 055301 (2021)ADS

Wise, Elliott S., Cox, B.T., Jaros, Jiri, Treeby, Bradley E.: Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods. J. Acoust. Soc. Am. 146, 278–288 (2019)ADS

Wu, L., Xie, L.-D., Zhang, J.-F.: Adomian decomposition method for nonlinear differential-difference equations. Commun. Nonlinear Sci. Numer. Simul. 14, 12–18 (2009)ADSMathSciNet

Younas, Usman., Younis, M., Seadawy, Aly R., Rizvi, S.T.R.: Optical solitons and closed form solutions to (3+1)-dimensional resonant Schrodinger equation, Int. J. Mod. Phys. B, 34(30): 2050291 (16 pages) (2020)

Zeković, S., Muniyappan, A., Zdravković, S., Kavitha, L.: Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules. Chin. Phys. B 23, 020504 (2014)

Zhao, W., Bourkoff, E.: Interactions between dark solitons. Opt. Lett. 14, 1371–1373 (1989)ADS

Zhao, W., Bourkoff, E.: Generation, propagation, and amplification of dark solitons. J. Opt. Soc. Am. B 9, 1134–1144 (1992)ADS

Zhao, L.C., Li, S.C., Ling, L.: W-shaped solitons generated from a weak modulation in the Sasa-Satsuma equation. Phys. Rev. E 93, 032215 (2016)ADSMathSciNet

Zhou, Q.: Chin. Phys. Lett. 39, 010501 (2022)ADS

Title: Chirped dark soliton propagation in optical fiber under a self phase modulation and a self-steepening effect for higher order nonlinear Schrödinger equation
Authors: A. Muniyappan
E. Parasuraman
Aly R. Seadawy
J. B. Sudharsan
Publication date: 01-05-2024
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 5/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-024-06358-y

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 5/2024

Cosine-Gaussian breathers controlled by the initial conditions in highly nonlocal media

New solitary wave solutions to Biswas–Milovic and resonant nonlinear Schrödinger equations

Optical properties and broadband radio frequencies dielectric performance of solution cast-hot pressed PVDF/PMMA/BaTiO3 nanocomposite films

Dynamic study of qualitative analysis, traveling waves, solitons, bifurcation, quasiperiodic, and chaotic behavior of integrable kuralay equations

Numerical solutions and analytical methods for the Kuralay equation: a path to understanding integrable systems

Complex behaviors and various soliton profiles of (2+1)-dimensional complex modified Korteweg-de-Vries Equation