Ir al contenido

Documat

Analyzing Abundant Optical Soliton Solutions for Coupled Nonlinear Helmholtz System Arising in Optics Communication

  • Sajid Ali [1] ; Shafiq Ahmad [1] ; Aman Ullah [1] ; Shabir Ahmad [2]
    1. [1] University of Malakand

      University of Malakand

      Pakistán

    2. [2] University of Campania “Luigi Vanvitelli”
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this article, we extract some optical soliton solutions for the coupled nonlinear Helmholtz system by utilizing the two effective analytical techniques, i.e. complete discriminant system method and enhanced modified extended tanh function method.

      The coupled nonlinear Helmholtz system has many applications in various fields of science such as optical fiber, photonic device, plasmonics, fluid dynamics, plasma physics, and technology. The achieved solutions are structured in exponential, trigonometric, hyperbolic, and Jacobi elliptic function solutions. Different soliton solutions like dark, bright, singular bright, singular periodic, W-M-shaped soliton solutions are obtained. Additionally, the reliability and effectiveness of the applied methodologies, some of the achieved solutions are visualized in 3D and contour representation by choosing well parameters values. The comparison of the achieved results with the solutions obtained in the published literature are discussed, proving that the derived solutions have not been studied previously in the published works. This demonstrates that the suggested methods in this study are more reliable, powerful, effective, and can be implemented to more high and complex non-integrable systems.

  • Referencias bibliográficas
    • 1. Wang, C.: Exact solutions of the steady-state Navier–Stokes equations. Annu. Rev. Fluid Mech. 23(1), 159–177 (1991)
    • 2. Melih, C., Ismail, O., Aydin, S., Abdulkadir, S.T., Abdullahi, Y., Mustafa, B.: Optical solitons of the (2+1)-dimensional Biswas–Milovic...
    • 3. Bulanov, S.V., Sasorov, F., Pegoraro, H., Kadlecová, S.S., Bulanov, T., Zh Esirkepov, N.N., Rosanov, P.V., Korn, G.: Electromagnetic solitons...
    • 4. Qi, Y., Manafian, J., Sulieman, K.M., Manafian, J., Kumar, A.: Multi wave solutions and wave propagation in plasma physics over the Gilson–Pickering...
    • 5. Xingxing, W., Jalil, M., Gurpreet, S., Baharak, E., Abdullah, A., Ali, K., Mohammad, A., Noor, A.A.: Different lump k-soliton solutions...
    • 6. Qiaoling, Y., Jalil, M., Khaled, H.M., Abdullah, A.: Abundant exact traveling wave solutions and modulation instability analysis to the...
    • 7. Lan, L., Manafian, J., Eslami, B., Hussein, A.: Homoclinic and N-soliton solutions to variablecoefficient KP equation arising two-temperature...
    • 8. Cheng, J., Manafian, J., Singh, G., Yadav, A.: Interaction between soliton and periodic solutions and the stability analysis to the Gilson–Pickering...
    • 9. Kumar, S., Mohan, B.: A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized...
    • 10. Kumar, S., Mohan, B., Kumar, A.: Generalized fifth-order nonlinear evolution equation for the Sawada– Kotera, Lax, and Caudrey–Dodd–Gibbon...
    • 11. Kumar, S., Kumar, A.: Newly generated optical wave solutions and dynamical behaviors of the highly nonlinear coupled Davey–Stewartson...
    • 12. Hamid, I., Kumar, S.: Symbolic computation and Novel solitons, traveling waves and soliton-like solutions for the highly nonlinear (2+1)-dimensional...
    • 13. Wang, K.J., Liu, X.L., Shi, F., Li, G.: Bifurcation and sensitivity analysis, chaotic behaviors, variational principle, Hamiltonian and...
    • 14. Ahmad, S., Ahmad, S., Khan, M.A., Ullah, A.: Exploration of optical solitons of a hyperbolic nonlinear Schrödinger equation. Opt Quantum...
    • 15. Abdullah, A., Sibel, Y.: Soliton wave parameter estimation with the help of artificial neural network by using the experimental data carried...
    • 16. Mostafa, M.A., Khater: Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation. Heliyon 9(2) (2023)
    • 17. Arshed, S., Akram, G., Sadaf, M., Khan, A.: Solutions of (3+1)-dimensional extended quantum nonlinear Zakharov–Kuznetsov equation...
    • 18. Khater, M.A.M.: A hybrid analytical and numerical analysis of ultra-short pulse phase shifts. Chaos, Solitons Fractals 169, 113232 (2023)
    • 19. Ozdemir, N., Secer, A., Bayram, M.: Extraction of soliton waves from the longitudinal wave equation with local M-truncated derivatives....
    • 20. Wang, K.J., Liu, J.H.: Mathematical model and the solution of the capillary vibration in a nanoscale deformable. Math. Methods Appl. Sci....
    • 21. Wang, K.J.: The generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation: resonant multiple soliton, N-soliton, soliton...
    • 22. Wang, K.J., Shi, F., Li, S., Xu, P.: Dynamics of resonant soliton, novel hybrid interaction, complex N-soliton and the abundant wave solutions...
    • 23. Kudryashov, N.A.: One method for 9nding exact solutions of nonlinear di5erential equations. Commun. Nonlinear Sci. Numer. Simul. 17(6),...
    • 24. Demiray, S. Tuluce, Pandir, Y., Bulut, H.: Generalized Kudryashov method for time–fractional differential equations. Abst. Appl. Anal....
    • 25. Zayed, E., Moatimid, G., Al-Nowehy, A.-G.: The generalized Kudryashov method and its applications for solving nonlinear PDEs in mathematical...
    • 26. Kheir, H., Jabbari, A., Yildirim, A., Alomari, A.: He’s semi–inverse method for soliton solutions of Boussinesq system. World J. Model....
    • 27. Alqahtani, R.T., Babatin, M.M., Biswas, A.: Bright optical solitons for Lakshmanan–Porsezian–Daniel model by semiinverse variational principle....
    • 28. He, J.-H., Wu, X.-H.: Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30(3), 700–708 (2006)
    • 29. Wu, X.-H.B., He, J.-H.: Solitary solutions, periodic solutions and compacton–like solutions using the Exp-function method. Comput. Math....
    • 30. Akbulut, A., Kaplan, M.: Auxiliary equation method for time-fractional differential equations with conformable derivative. Comput. Math....
    • 31. Li, B.-Q., Ma, Y.-L.: Loop-like periodic waves and solitons to the Kraenkel–Manna–Merle system in ferrites. J. Electromagn. Waves Appl....
    • 32. Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas– Milovic equation by extended trial equation...
    • 33. Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Zaka Ullah, M., Zhou, Q., Triki, H., Moshokoa, S.P., Biswas, A.: Optical solitons with anti-cubic...
    • 34. Akram, U., Tang, Z., Althobaiti, S., Althobait, A.: Dynamics of optical dromions in concatenation model. Nonlinear Dyn. 1–21 (2024)
    • 35. Khoso, I.A., Katbar, N.M., Akram, U.: Optical dromions for spatiotemporal fractional nonlinear system in quantum mechanics. Quantum Rep....
    • 36. Seadawy, A.R., Akram, U., Rizvi, S.T.: Dispersive optical solitons along with integrability test and one soliton transformation for saturable...
    • 37. Wazwaz, A.-M.: The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl. Math. Comput. 188(2), 1467–1475...
    • 38. Wazwaz, A.-M.: The tanh-coth method for new compactons and solitons solutions for the K (n, n) and the K (n+1, n+1) equations....
    • 39. Kumar, A., Kumar, S.: Dynamic nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov–Novikov–Wang equation using...
    • 40. Korkmaz, A., Hepson, O.E., Hosseini, K., Rezazadeh, H., Eslami, M.: Sine–Gordon expansion method for exact solutions to conformable time...
    • 41. Bulut, H., Sulaiman, T.A., Demirdag, B.: Dynamics of soliton solutions in the chiral nonlinear Schrödinger equations. Nonlinear Dyn. 91(3),...
    • 42. Baskonus, H.M., Sulaiman, T.A., Bulut, H.: Novel complex and hyperbolic forms to the strain wave equation in microstructured solids. Opt....
    • 43. Seadawy, A.R., Ahmed, H.M., Rabie, W.B., Biswas, A.: An alternate pathway to solitons in magnetooptic waveguides with triple-power law...
    • 44. Ghayad, M.S., Badra, N.M., Ahmed, H.M., Rabie, W.B.: Derivation of optical solitons and other solutions for nonlinear Schrödinger equation...
    • 45. Rabie, W.B., Ahmed, H.M., Akgül, A.: Derivation of optical solitons for perturbed highly dispersive conformable fractional nonlinear Schrödinger...
    • 46. Khalil, T.A., Badra, N., Ahmed, H.M., Rabie,W.B.: Bright solitons for twin-core couplers and multiplecore couplers having polynomial law...
    • 47. Zhang, H., Manafian, J., Singh, G., Ilhan, O.A., Zekiy, A.O.: N-lump and interaction solutions of localized waves to the (2+1)-dimensional...
    • 48. Zhang, M., Xie, X., Manafian, J., Ilhan, O.A., Singh, G.: Characteristics of the new multiple rogue wave solutions to the fractional generalized...
    • 49. Donfack, E.F., Nguenang, J.P., Nana, L.: On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order...
    • 50. Fendzi-Donfack, E., Tala-Tebue, E.: Mustafa Inc, A., Kenfack-Jiotsa, J.P., Nguenang, L. Nana: Dynamical behaviours and fractional alphabetical-exotic...
    • 51. Usman, M., Hussain, A., Ali, H., Zaman, F., Abbas, N.: Dispersive modified Benjamin–Bona–Mahony and Kudryashov–Sinelshchikov equations:...
    • 52. Bilal, M., Haris, H., Waheed, A., Faheem, M.: The analysis of exact solitons solutions in monomode optical fibers to the generalized nonlinear...
    • 53. Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission...
    • 54. Fendzi-Donfack, E., Kumar, D., Tala-Tebue, E., Nana, L., Nguenang, J.P., Kenfack-Jiotsa, A.: Construction of exotical soliton-like for...
    • 55. Demirbilek, U., Nadeem, M., Çelik, F.M., Bulut, H., Senol, M.: Generalized extended (2+1)- dimensional Kadomtsev–Petviashvili equation...
    • 56. Akinyemi, L., Houwe, A., Abbagari, S., Wazwaz, A.-M., Alshehri, H.M., Osman, M.S.: Effects of the higher-order dispersion on solitary...
    • 57. Qiaoling, Y., Jalil, M., Khaled, H., Mahmoud, Abdullah, A.: Abundant exact traveling wave solutions and modulation instability analysis...
    • 58. Abraham, N.B., Firth, W.J.: Overview of transverse effects in nonlinear-optical systems. J. Opt. Sot. Am. B 7, 951–962 (1990)
    • 59. Singh, S., Kaur, L., Sakthivel, R., Murugesan, K.: Computing solitary wave solutions of coupled nonlinear Hirota and Helmholtz equations....
    • 60. Alsaud, H., Youssoufa, M., Inc, M., Inan, I.E., Bicer, H.: Some optical solitons and modulation instability analysis of (3+1)-dimensional...
    • 61. Zhang, K., Han, T., Li, Z.: New single traveling wave solution of the Fokas system via complete discrimination system for polynomial method....
    • 62. Ozisik, M., Bayram, M., Secer, A., Cinar, M.: On the analytical soliton solutions of (1+1)-dimensional complex coupled nonlinear Higgs...
    • 63. Tamilselvan, K., Kanna, T., Khare, A.: Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations. Commun....
    • 64. Sakkaravarthi, K., Johnpillai, A.G., Devi, A.D., Kanna, T., Lakshmanan, M.: Lie symmetry analysis and group invarient solutions of the...
    • 65. Tipu, G.H., Faridi, W.A., Rizk, D., Myrzakulova, Z., Myrzakulov, R., Akinyemi, L.: The optical exact soliton solutions of Shynaray-IIA...
    • 66. Tarla, S., Ali, K.K., Yilmazer, R.: Newly modified unified auxiliary equation method and its applications. Opt.-Int. J. Light Electron....
    • 67. Sa ˘gulam, F.N.K., Malik, S.: Various traveling wave solutions for (2+1)-dimensional extended Kadomtsev–Petviashvili equation using...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno