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Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods

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Abstract

The Ginzburg–Landau equation (GLE) plays an important role in discrete solitons laser array lattices. In this manuscript, the analytical solution for GLE which is a discrete analogue of laser array using non-perturbation methods is represented. The laser array for stability analysis of time-dependent solution in terms of damping and coupling is investigated. Further, GLE equation for periodic travelling wave solution with homotopy perturbation method and variational iteration method is derived. These methods provide a straightforwardly computable, readily demonstrable and rapidly convergent solution. For the sake of the consistency, validation and effectiveness of these methods, a convergence of GLE has also been revealed.

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References

  1. Pottoo, S.N., Goyal, R., Gupta, A.: Development of 32‑GBaud DP‑QPSK free space optical transceiver using homodyne detection and advanced digital signal processing for future optical networks. Opt. Quantum Electron. 52(496), (2020)

  2. Goyal, R., Kaler, R.: A novel architecture of hybrid (WDM/TDM) passive optical networks with suitable modulation format. Opt. Fiber Technol. 18(6), 518–522 (2012)

    Article  Google Scholar 

  3. Goyal, R., Kaler, R.S.: Investigation on polarization dependent bidirectional hybrid (WDM/TDM) utilizing QAM modulation with different amplifiers. Optoelectron. Adv. Mater Rapid Commun. Natl. Inst. 8(8), 631–634 (2014)

    Google Scholar 

  4. Kumar, C., Goyal, R.: Analysis of proposed hybrid amplifier model for single to multi-channel WDM optical system at 10 Gbps with 100 GHz of channel spacing. Int. J. Inf. Technol. (in press) (2017)

  5. Wang, Z., Li, Te., Yang, G., Song, Y.: High power, high efficiency continuous-wave 808 nm laser diode arrays. Opt. Laser Technol. 97, 297–301 (2017)

    Article  Google Scholar 

  6. Li, J., Cao, J., Xu, X.: Effects of phase errors on phase locking of all-fiber laser arrays. Opt. Laser Technol. 47, 372–378 (2013)

    Article  Google Scholar 

  7. Guo, F., Dan, Lu., Zhang, R., Liu, S., Sun, M., Kan, Q., Ji, C.: A 1.3-μm four-channel directly modulated laser array fabricated by SAGUpper-SCH technology. Opt. Commun. 383, 577–580 (2017)

    Article  Google Scholar 

  8. Zhou, L., Duan, K.: Stability in a general coupled laser array. Optik 123, 2187–2190 (2012)

    Article  Google Scholar 

  9. Thomson, S.J., Durey, M., Rosales, R.R.: Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice. Phys. Rev. E 103, 062215 (2021)

    Article  MathSciNet  Google Scholar 

  10. Akram, G., Sadaf, M., Mariyam, H.: A comparative study of the optical solitons for the fractional complex Ginzburg–Landau equation using different fractional differential operators. Optik 256, 168626 (2022)

    Article  Google Scholar 

  11. Hennig, D., Karachalios, N.I.: Dynamics of nonlocal and local discrete Ginzburg–Landau equations: global attractors and their congruence. Nonlinear Anal. 215, 112647 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  12. Neveen, G., Ahmed, H.E., El-Azabb, M.S., Obayya, S.S.A.: Pseudo-spectral approach for extracting optical solitons of the complex Ginzburg Landau equation with six nonlinearity forms”. Optik 254, 168662 (2022)

    Article  Google Scholar 

  13. Mukai, D.: Mirror symmetry of nonabelian Landau-Ginzburgorbifolds with loop type potentials. J. Geom. Phys. 159, 103877 (2021)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Malomed, B.A.: New findings for the old problem: Exact solutions for domain walls in coupled real Ginzburg–Landau equations. Phys. Lett. A 422, 127802 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fan, J., Samet, B., Zhou, Y.: Uniform regularity for a 3D time-dependent Ginzburg–Landau model in superconductivity. Comput. Math. Appl. 75(9), 3244–3248 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yang, L., Xueke, Pu.: Large deviations for stochastic 3D cubic Ginzburg–Landau equation with multiplicative noise. Appl. Math. Lett. 48, 41–46 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Oskoee, E.N.: Computing properties of materials based on the Ginzburg-Landau equation. Comput. Sci. Eng. 9(2), 84–95 (2007)

    Article  Google Scholar 

  19. Rani, M., Bhatti, H.S., Singh, V.: Exact solitary wave solution for higher order nonlinear schrodinger equation using He’s variational iteration method. Opt. Eng. 56(11), 116103 (2017)

    Article  Google Scholar 

  20. Rani, M., Bhatti, H.S., Singh, V.: Performance analysis of spectral amplitude coding optical code division multiple access system using modified double weight codes with adomian decomposition method. J. Opt. Commun. 39(4), 1–8 (2017)

    Google Scholar 

  21. Tozar, A.: New analytical solutions of fractional complex Ginzburg–Landau equation. Univ. J. Math. Appl. 3(3), 129–132 (2020)

    Article  Google Scholar 

  22. Thomson, S.J., Durey, M., Rosales, R.R.: Discrete and periodic complex Ginzburg–Landau equation for a hydrodynamic active lattice. Phys. Rev. E 103, 062215 (2021)

    Article  MathSciNet  Google Scholar 

  23. Naghshband, S., Fariborzi Araghi, M.A.: Solving the cubic complex Ginzburg–Laundau equation by Homotopy analysis method. Indian J. Sci. Technol. 13(24), 2387–2403 (2020)

    Article  Google Scholar 

  24. Zhang, X., Chai, J., Huang, J., Chen, Z., Li, Y., Malomed, B.A.: Discrete solitons and scattering of lattice waves in guiding arrays with a nonlinear PT-symmetric defect. Opt. Express 22(11), 13927–13939 (2014)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Kanya Maha Vidyalaya, Jalandhar, Punjab, India

    Monika Rani

  2. I K Gujral Punjab Technical University, Jalandhar, Punjab, India

    Vikramjeet Singh & Rakesh Goyal

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  1. Monika Rani
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  2. Vikramjeet Singh
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  3. Rakesh Goyal
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Rani, M., Singh, V. & Goyal, R. Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods. Photon Netw Commun 46, 108–111 (2023). https://doi.org/10.1007/s11107-023-01005-0

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