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Erschienen in: Optical and Quantum Electronics 5/2024

01.05.2024

Optical devices: motion via breathers, rogue waves and rational solitons

verfasst von: Ujala Rehman, Sarfaraz Ahmed, Ali M. Mubaraki

Erschienen in: Optical and Quantum Electronics | Ausgabe 5/2024

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Abstract

The main focus is on using the logarithmic transformation and symbolic computation with ansatz functions scheme to analyse solitons theoretically in the ring-cavity fibre laser system with carbon nanotubes acting as saturable absorber. The system is renowned as a non-standard Schrödinger model through the coefficients combined real and imaginary numbers. The governing model is used in ring-cavity fibre laser system using carbon nanotubes as saturable absorbers. We obtained Chirp-free soliton, Homoclinic breathers, M-shaped rational solitons, Multiwaves and their dynamics are revealed in plots by choosing the proper values of parameters. Additionally, four categories of interaction of M-shaped rational soliton with rogue wave, periodic wave and kink wave are studied. we accomplished the new structures and very fascinating interactional phenomena of M shaped soliton with kink waves. Furthermore, through a mixture of quadratic, cosine and hyperbolic transformations we obtained periodic cross rational solutions and via three wave transformation we generated multiwave solutions.

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Zurück zum Zitat Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique. Chaos Solitons Fractals 144, 110669 1–12 (2021a)MathSciNet Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique. Chaos Solitons Fractals 144, 110669 1–12 (2021a)MathSciNet
Zurück zum Zitat Seadawy, A.R., Rehman, S.U., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer–Chree equation. Phys. Scr. 96(4), 045202 1–13 (2021b)ADS Seadawy, A.R., Rehman, S.U., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer–Chree equation. Phys. Scr. 96(4), 045202 1–13 (2021b)ADS
Zurück zum Zitat Seadawy, A.R., Rizvi, S.T.R., Ahmad, S., Younis, M., Baleanu, D.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation. Open Phys. 19(1), 1–10 (2021c) Seadawy, A.R., Rizvi, S.T.R., Ahmad, S., Younis, M., Baleanu, D.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation. Open Phys. 19(1), 1–10 (2021c)
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Zurück zum Zitat Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Weierstrass and Jacobi elliptic, bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation. Chaos Solitons Fractals 160, 112258 1–20 (2022a) Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Weierstrass and Jacobi elliptic, bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation. Chaos Solitons Fractals 160, 112258 1–20 (2022a)
Zurück zum Zitat Seadawy, A.R., Ahmed, S., Rizvi, S.T., Ali, K.: Various forms of lumps and interaction solutions to generalized Vakhnenko Parkes equation arising from high-frequency wave propagation in electromagnetic physics. J. Geom. Phys. 176, 104507 1–22 (2022b)MathSciNet Seadawy, A.R., Ahmed, S., Rizvi, S.T., Ali, K.: Various forms of lumps and interaction solutions to generalized Vakhnenko Parkes equation arising from high-frequency wave propagation in electromagnetic physics. J. Geom. Phys. 176, 104507 1–22 (2022b)MathSciNet
Zurück zum Zitat Seadawy, A.R., Ahmed, S., Rizvi, S.T., Ali, K.: Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system. Chaos Solitons Fractals 161, 112307 1–16 (2022c)MathSciNet Seadawy, A.R., Ahmed, S., Rizvi, S.T., Ali, K.: Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system. Chaos Solitons Fractals 161, 112307 1–16 (2022c)MathSciNet
Zurück zum Zitat Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Multiple lump, generalized breathers, Akhmediev breather, manifold periodic and rogue wave solutions for generalized Fitzhugh–Nagumo equation: applications in nuclear reactor theory. Chaos Solitons Fractals 161, 112326 1–25 (2022d)MathSciNet Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Multiple lump, generalized breathers, Akhmediev breather, manifold periodic and rogue wave solutions for generalized Fitzhugh–Nagumo equation: applications in nuclear reactor theory. Chaos Solitons Fractals 161, 112326 1–25 (2022d)MathSciNet
Zurück zum Zitat Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Solitons collision and multi-peak solutions for a new (3+ 1)-dimensional NLSE describing pulse propagation in optical fibers. Opt. Quant. Electron. 55(5), 467 1–24 (2023a) Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Solitons collision and multi-peak solutions for a new (3+ 1)-dimensional NLSE describing pulse propagation in optical fibers. Opt. Quant. Electron. 55(5), 467 1–24 (2023a)
Zurück zum Zitat Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Analytical solutions along with grey-black optical solitons under the influence of self-steepening effect and third order dispersion. Opt. Quant. Electron. 55(3), 288 1–20 (2023b) Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Analytical solutions along with grey-black optical solitons under the influence of self-steepening effect and third order dispersion. Opt. Quant. Electron. 55(3), 288 1–20 (2023b)
Zurück zum Zitat Seadawy, A.R., Rizvi, S.T., Ahmed, S., Batool, T.: Propagation of W-shaped and M-shaped solitons with multi-peak interaction for ultrashort light pulse in fibers. Opt. Quant. Electron. 55(3), 1–23 (2023c) Seadawy, A.R., Rizvi, S.T., Ahmed, S., Batool, T.: Propagation of W-shaped and M-shaped solitons with multi-peak interaction for ultrashort light pulse in fibers. Opt. Quant. Electron. 55(3), 1–23 (2023c)
Zurück zum Zitat Seadawy, A.R., Ahmed, S., Rizvi, S.T., Nazar, K.: Applications for mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation in water wave flumes and optical fibers. Opt. Quant. Electron. 55(1), 34 1–22 (2023d) Seadawy, A.R., Ahmed, S., Rizvi, S.T., Nazar, K.: Applications for mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation in water wave flumes and optical fibers. Opt. Quant. Electron. 55(1), 34 1–22 (2023d)
Zurück zum Zitat Seadawy, A.R., Ahmad, A., Rizvi, S.T., Ahmed, S.: Bifurcation solitons, Y-type, distinct lumps and generalized breather in the thermophoretic motion equation via graphene sheets. Alex. Eng. J. 87, 374–388 (2024) Seadawy, A.R., Ahmad, A., Rizvi, S.T., Ahmed, S.: Bifurcation solitons, Y-type, distinct lumps and generalized breather in the thermophoretic motion equation via graphene sheets. Alex. Eng. J. 87, 374–388 (2024)
Zurück zum Zitat Seaway, A.R., Rizvi, S.T., Ahmad, A., Ahmed, S.: Multiwave, rogue wave, periodic wave, periodic cross-lump wave, periodic cross-kink wave, lump soliton, breather lump, homoclinic breather, periodic cross-kink, M-shaped rational solutions and their interactions for the Degasperis-Procesi equation. Int. J. Mod. Phys. B 37(18), 2350172 1–30 (2023a)ADS Seaway, A.R., Rizvi, S.T., Ahmad, A., Ahmed, S.: Multiwave, rogue wave, periodic wave, periodic cross-lump wave, periodic cross-kink wave, lump soliton, breather lump, homoclinic breather, periodic cross-kink, M-shaped rational solutions and their interactions for the Degasperis-Procesi equation. Int. J. Mod. Phys. B 37(18), 2350172 1–30 (2023a)ADS
Zurück zum Zitat Seaway, A.R., Rizvi, S.T., Ahmad, A., Ahmed, S.: Multiwave, rogue wave, periodic wave, periodic cross-lump wave, periodic cross-kink wave, lump soliton, breather lump, homoclinic breather, periodic cross-kink, M-shaped rational solutions and their interactions for the Degasperis-Procesi equation. Int. J. Mod. Phys. B 37, 2350172 1–30 (2023b)ADS Seaway, A.R., Rizvi, S.T., Ahmad, A., Ahmed, S.: Multiwave, rogue wave, periodic wave, periodic cross-lump wave, periodic cross-kink wave, lump soliton, breather lump, homoclinic breather, periodic cross-kink, M-shaped rational solutions and their interactions for the Degasperis-Procesi equation. Int. J. Mod. Phys. B 37, 2350172 1–30 (2023b)ADS
Zurück zum Zitat Shafqat-ur-Rehman, Ahmad, J.: Stability analysis and novel optical pulses to Kundu-Mukherjee-Naskar model in birefringent fibers. Int. J. Mod. Phys. B 37, 2450192 1–13 (2023) Shafqat-ur-Rehman, Ahmad, J.: Stability analysis and novel optical pulses to Kundu-Mukherjee-Naskar model in birefringent fibers. Int. J. Mod. Phys. B 37, 2450192 1–13 (2023)
Zurück zum Zitat Shen, S., Yang, Z.J., Pang, Z.G., Ge, Y.R.: The complex-valued astigmatic cosine-Gaussian soliton solution of the nonlocal nonlinear Schrödinger equation and its transmission characteristics. Appl. Math. Lett. 125, 107755 1–14 (2022) Shen, S., Yang, Z.J., Pang, Z.G., Ge, Y.R.: The complex-valued astigmatic cosine-Gaussian soliton solution of the nonlocal nonlinear Schrödinger equation and its transmission characteristics. Appl. Math. Lett. 125, 107755 1–14 (2022)
Zurück zum Zitat Song, L.M., Yang, Z.J., Li, X.L., Zhang, S.M.: Coherent superposition propagation of Laguerre–Gaussian and Hermite–Gaussian solitons. Appl. Math. Lett. 102, 106114 1-12 (2020)MathSciNet Song, L.M., Yang, Z.J., Li, X.L., Zhang, S.M.: Coherent superposition propagation of Laguerre–Gaussian and Hermite–Gaussian solitons. Appl. Math. Lett. 102, 106114 1-12 (2020)MathSciNet
Zurück zum Zitat Subramanian, K., Alagesan, T., Mahalingam, A., Mani Rajan, M.S.: Propagation properties of optical soliton in an erbium-doped tapered parabolic index nonlinear fiber: soliton control. Nonlinear Dyn. 87, 1575–1587 (2017) Subramanian, K., Alagesan, T., Mahalingam, A., Mani Rajan, M.S.: Propagation properties of optical soliton in an erbium-doped tapered parabolic index nonlinear fiber: soliton control. Nonlinear Dyn. 87, 1575–1587 (2017)
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Zurück zum Zitat Tariq, K.U., Zainab, H., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Abd Allah, A.M.: On some novel optical wave solutions to the paraxial M-fractional nonlinear Schrödinger dynamical equation. Opt. Quant. Electron. 53(5), 1–14 (2021) Tariq, K.U., Zainab, H., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Abd Allah, A.M.: On some novel optical wave solutions to the paraxial M-fractional nonlinear Schrödinger dynamical equation. Opt. Quant. Electron. 53(5), 1–14 (2021)
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Zurück zum Zitat Wazwaz, A.M.: Bright and dark optical solitons of the (2+ 1)-dimensional perturbed nonlinear Schrödinger equation in nonlinear optical fibers. Optik 251, 168334 1–8 (2022)ADS Wazwaz, A.M.: Bright and dark optical solitons of the (2+ 1)-dimensional perturbed nonlinear Schrödinger equation in nonlinear optical fibers. Optik 251, 168334 1–8 (2022)ADS
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Zurück zum Zitat Zhang, B., Xu, Z.L., He, Y.B., Abouali, S., Garakani, M.A., Heidari, E.K., Kim, J.K.: Exceptional rate performance of functionalized carbon nanofiber anodes containing nanopores created by (Fe) sacrificial catalyst. Nano Energy 4(1), 88–96 (2014) Zhang, B., Xu, Z.L., He, Y.B., Abouali, S., Garakani, M.A., Heidari, E.K., Kim, J.K.: Exceptional rate performance of functionalized carbon nanofiber anodes containing nanopores created by (Fe) sacrificial catalyst. Nano Energy 4(1), 88–96 (2014)
Zurück zum Zitat Zou, Z., Guo, R.: The Riemann–Hilbert approach for the higher-order Gerdjikov–Ivanov equation, soliton interactions and position shift. Commun. Nonlinear Sci. Numer. Simul. 124, 107316 1–12 (2020)MathSciNet Zou, Z., Guo, R.: The Riemann–Hilbert approach for the higher-order Gerdjikov–Ivanov equation, soliton interactions and position shift. Commun. Nonlinear Sci. Numer. Simul. 124, 107316 1–12 (2020)MathSciNet
Metadaten
Titel
Optical devices: motion via breathers, rogue waves and rational solitons
verfasst von
Ujala Rehman
Sarfaraz Ahmed
Ali M. Mubaraki
Publikationsdatum
01.05.2024
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 5/2024
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-024-06577-3

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