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Stability, modulation instability and explicit-analytical solutions for the Hamiltonian amplitude equation

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Abstract

The Hamiltonian amplitude equation that describes the transmissions of wire optical technology along wave propagation in the physics linked disciplines can be solved by utilizing the unique analytical and semi-analytical approaches namely the polynomial expansion method and the Adomian decomposition technique. Various types of soliton solutions are attained that express different behaviours including singular and v-shaped soliton solutions behaviour. The developed solutions are highly important in dealings the wave behaviour in mathematical physics related fields and in the transmission of optical fibers. The approaches applied in this paper are not utilized in given model so we apply these strategies to attain the soliton solutions. Hence we conclude the the results attained are unique, robust and newly made that proves novelty of the work. Furthermore, we study the stability plus the modulation instability of the given model. The 3D, contours, and 2D graphics are visualised to demonstrate the dynamical structures of the established results more efficiently.

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References

  • Abedi, M., Fangueiro, R., Correia, A.G., Shayanfar, J.: Smart geosynthetics and prospects for civil infrastructure monitoring: a comprehensive and critical review. Sustainability 15(12), 9258 (2023)

    Article  Google Scholar 

  • Ahmad, J., Rani, S.: Study of soliton solutions with different wave formations to model of nonlinear schrödinger equation with mixed derivative and applications. Opt. Quantum Electron. 55(13), 1195 (2023)

    Article  Google Scholar 

  • Ahmad, J., Rani, S., Turki, N.B., Shah, N.A.: Novel resonant multi-soliton solutions of time fractional coupled nonlinear schrödinger equation in optical fiber via an analytical method. Res. Phys. 52, 106761 (2023)

    Google Scholar 

  • Akram, G., Mahak, N.: Application of the first integral method for solving (1+ 1) dimensional cubic-quintic complex ginzburg-landau equation. Optik 164, 210–217 (2018)

    Article  ADS  Google Scholar 

  • Ali, M., Alquran, M., BaniKhalid, A.: Symmetric and asymmetric binary- solitons to the generalized two-mode kdv equation: novel findings for arbitrary nonlinearity and dispersion parameters. Res. Phys. 45, 106250 (2023)

    Google Scholar 

  • Ali, A., Ahmad, J., Javed, S.: Dynamic investigation to the generalized yu-toda-sasa-fukuyama equation using darboux transformation. Opt. Quantum Electron. 56(2), 166 (2024)

    Article  Google Scholar 

  • Alquran, M.: Classification of single-wave and bi-wave motion through fourth-order equations generated from the Ito model. Phys. Scr. 98 085207 (2023)

  • Alquran, M., Al Smadi, T.: Generating new symmetric bi-peakon and singular bi-periodic profile solutions to the generalized doubly dispersive equation. Opt. Quantum Electron. 55(8), 736 (2023)

    Article  Google Scholar 

  • Alquran, M., Alhami, R.: Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-kdv equation by means of hirotas bilinear method. Nonlinear Dyn. 109(3), 1985–1992 (2022)

    Article  Google Scholar 

  • Alquran, M., Ali, M., Gharaibeh, F., Qureshi, S.: Novel investigations of dual-wave solutions to the Kadomtsev-Petviashvili model involving secondorder temporal and spatial-temporal dispersion terms. Partial Differ. Equ. Appl. Math. 8, 100543 (2023)

    Article  Google Scholar 

  • Alquran, M., Najadat, O., Ali, M., Qureshi, S.: New kink-periodic and convex-concave-periodic solutions to the modified regularized long wave equation by means of modified rational trigonometric-hyperbolic functions. Nonlinear Eng. 12(1), 20220307 (2023)

    Article  ADS  Google Scholar 

  • Aluru, N.R., Aydin, F., Bazant, M.Z., Blankschtein, D., Brozena, A.H., de Souza, J.P., Elimelech, M., Faucher, S., Fourkas, J.T., Koman, V.B., et al.: Fluids and electrolytes under confinement in single-digit nanopores. Chem. Rev. 123(6), 2737–2831 (2023)

    Article  Google Scholar 

  • Bilal, M., Younis, M., Ahmad, J., Younas, U., et al.: Investigation of new solitons and other solutions to the modified nonlinear schrödinger equation in ocean engineering. J. Ocean Eng. Sci. (fourthcoming)

  • Bilal, M., Younas, U., Ren, J.: Dynamics of exact soliton solutions to the coupled nonlinear system using reliable analytical mathematical approaches. Commun. Theor. Phys. 73(8), 085005 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Bilal, M., Ren, J., Younas, U.: Stability analysis and optical soliton solutions to the nonlinear schrödinger model with efficient computational techniques. Opt. Quantum Electron. 53, 1–19 (2021)

    Article  Google Scholar 

  • Bilal, M., Ren, J., Inc, M., Alqahtani, R.T.: Dynamics of solitons and weakly ion-acoustic wave structures to the nonlinear dynamical model via analytical techniques. Opt. Quantum Electron. 55(7), 656 (2023)

    Article  Google Scholar 

  • Copie, F., Randoux, S., Suret, P.: The physics of the one-dimensional nonlinear schrödinger equation in fiber optics: Rogue waves, modulation instability and self-focusing phenomena. Rev. Phys. 5, 100037 (2020)

    Article  Google Scholar 

  • Fendzi-Donfack, E., Kenfack-Jiotsa, A.: Extended fans sub-ode technique and its application to a fractional nonlinear coupled network including multicomponentslc blocks. Chaos Solitons Fractals 177, 114266 (2023)

    Article  Google Scholar 

  • Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation. Eur. Phys. J. Plus 133, 1–11 (2018)

    Article  Google Scholar 

  • Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line. Nonlinear Dyn. 104, 691–704 (2021)

    Article  Google Scholar 

  • Fendzi-Donfack, E., Baduidana, M., Fotsa-Ngaffo, F., Kenfack-Jiotsa, A.: Construction of abundant solitons in a coupled nonlinear pendulum lattice through two discrete distinct techniques. Res. Phys. 52, 106783 (2023)

    Google Scholar 

  • Fendzi-Donfack, E., Tala-Tebue, E., Inc, M., Kenfack-Jiotsa, A., Nguenang, J., Nana, L.: Dynamical behaviours and fractional alphabetical-exotic solitons in a coupled nonlinear electrical transmission lattice including wave obliqueness. Opt. Quantum Electron. 55(1), 35 (2023)

    Article  Google Scholar 

  • Gao, W., Veeresha, P., Prakasha, D.G., Baskonus, H.M.: New numerical simulation for fractional Benney-lin equation arising in falling film problems using two novel techniques. Numer. Methods Partial Differ. Equ. 37(1), 210–243 (2021)

    Article  MathSciNet  Google Scholar 

  • Hameedullah, Rafiullah, Saifullah, S., Ahmad, S., Rahman, M.U.: Stability, modulation instability analysis and new travelling wave solutions of non-dissipative double-dispersive microstrain wave model within microstructured solids. Opt. Quantum Electron. 56(2), 223 (2024)

    Article  Google Scholar 

  • He, Q., Rahman, M.U., Xie, C.: Information overflow between monetary policy transparency and inflation expectations using multivariate stochastic volatility models. Appl. Math. Sci. Eng. 31(1), 2253968 (2023)

    Article  MathSciNet  Google Scholar 

  • Khan, A., Saifullah, S., Ahmad, S., Khan, M.A., Rahman, M.U.: Dynamical properties and new optical soliton solutions of a generalized nonlinear schrödinger equation. Eur. Phys. J. Plus 138(11), 1059 (2023)

    Article  Google Scholar 

  • Kumar, S., Niwas, M.: New optical soliton solutions of biswas–arshed equation using the generalised exponential rational function approach and Kudryashovs simplest equation approach. Pramana 96(4), 204 (2022)

  • Lei, J.: Driving model of electronic information system based on agent modeling and simulation. Appl. Math. Nonlinear Sci. 8(2) 1683–1694 (2023)

  • Liu, F., Feng, Y.: The modified generalized Kudryashov method for nonlinear space-time fractional partial differential equations of schrödinger type. Res. Phys. 53, 106914 (2023)

    Google Scholar 

  • Liu, F.-Y., Gao, Y.-T., Yu, X., Li, L.-Q., Ding, C.-C., Wang, D.: Lie group analysis and analytic solutions for a (2+ 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation in fluid mechanics and plasma physics. Eur. Phys. J. Plus 136(6), 656 (2021)

    Article  Google Scholar 

  • Lu, J., Hong, X.: Exact traveling wave solutions for generalized Camassaholm equation by polynomial expansion methods. Appl. Math. 7(14), 1599–1611 (2016)

    Article  Google Scholar 

  • Manafian, J., Heidari, S.: Periodic and singular kink solutions of the Hamiltonian amplitude equation. Adv. Math. Models Appl. 4(2), 134–149 (2019)

    Google Scholar 

  • Matoog, R., Salas, A.H., Alharbey, R., El-Tantawy, S.: Rational solutions to the cylindrical nonlinear schrödinger equation: Rogue waves, breathers, and Jacobi breathers solutions. J. Ocean Eng. Sci. (fourthcoming)

  • Raheel, M., Zafar, A., Cevikel, A., Rezazadeh, H., Bekir, A.: Exact wave solutions of truncated m-fractional new Hamiltonian amplitude equation through two analytical techniques. Int. J. Modern Phys. B 37(01), 2350003 (2023)

    Article  ADS  Google Scholar 

  • Saifullah, S., Ahmad, S., Alyami, M.A., Inc, M.: Analysis of interaction of lump solutions with kink-soliton solutions of the generalized perturbed kdv equation using hirota-bilinear approach. Phys. Lett. A 454, 128503 (2022)

    Article  MathSciNet  Google Scholar 

  • Samaniego, E., Anitescu, C., Goswami, S., Nguyen-Thanh, V.M., Guo, H., Hamdia, K., Zhuang, X., Rabczuk, T.: An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications. Comput. Methods Appl. Mech. Eng. 362, 112790 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  • Seadawy, A.R., Rehman, S., Younis, M., Rizvi, S., Althobaiti, S., Makhlouf, M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with pochhammer-chree equation. Phys. Scr. 96(4), 045202 (2021)

    Article  ADS  Google Scholar 

  • Siddique, I., Abdal, S., Din, I.S.U., Awrejcewicz, J., Paw lowski, W., Hussain, S.: Significance of concentration-dependent viscosity on the dynamics of tangent hyperbolic nanofluid subject to motile microorganisms over a nonlinear stretching surface. Sci. Rep. 12(1), 12765 (2022)

    Article  ADS  Google Scholar 

  • Younas, U., Bilal, M., Ren, J.: Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion. Opt. Quantum Electron. 53, 1–25 (2021)

    Article  Google Scholar 

  • Yunus, A.O., Olayiwola, M.O., Omoloye, M.A., Oladapo, A.O.: A fractional order model of lassa disease using the laplace-adomian decomposition method. Healthc. Anal. 3, 100167 (2023)

  • Zafar, A., Raheel, M., Ali, K.K., Razzaq, W.: On optical soliton solutions of new Hamiltonian amplitude equation via Jacobi elliptic functions. Eur. Phys. J. Plus 135(8), 674 (2020)

    Article  Google Scholar 

  • Zhao, Y.-W., Xia, J.-W., Lü, X.: The variable separation solution, fractal and chaos in an extended coupled (2+ 1)-dimensional burgers system. Nonlinear Dyn. 108(4), 4195–4205 (2022)

    Article  Google Scholar 

  • Zhu, X., Xia, P., He, Q., Ni, Z., Ni, L.: Coke price prediction approach based on dense gru and opposition-based learning salp swarm algorithm. Int. J. Bio-Inspir. Comput. 21(2), 106–121 (2023)

    Article  Google Scholar 

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Acknowledgements

The authors extend their appreciation to Prince Sattam bin Abdulaziz University, Saudi Arabia for funding this research work through the project number (PSAU/2024/01/823183).

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Authors and Affiliations

  1. Department of Mathematics, Mirpur University of Science and Technology, Mirpur, AJK, 10250, Pakistan

    Kalim U. Tariq & S. M. Raza Kazmi

  2. Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030, Eskisehir, Turkey

    Ahmet Bekir

  3. Department of Computer Science, Prince Sattam Bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia

    Ali Altalbe

  4. Faculty of Computing and Information Technology, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    Ali Altalbe

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  1. Kalim U. Tariq
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  2. Ahmet Bekir
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  4. S. M. Raza Kazmi
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Contributions

KUT: Methodology, conceptualization, software, resources and planning. AB: Supervision, project administration, visualizations, review and editing. AA: Funding acquisition, investigation, validation, review and editing. SMRK: Scientific computing, formal analysis and investigation, writing original draft.

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Correspondence to Kalim U. Tariq or Ahmet Bekir.

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Tariq, K.U., Bekir, A., Altalbe, A. et al. Stability, modulation instability and explicit-analytical solutions for the Hamiltonian amplitude equation. Opt Quant Electron 56, 840 (2024). https://doi.org/10.1007/s11082-024-06466-9

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