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M-shaped and other exotic solitons generated by cubic-quintic saturable nonlinearities in a nonlinear electrical transmission network with higher-order dispersion effects

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  • Essama, Bedel Giscard Onana
  • Bisse, Jacquie Therese Ngo
  • Essiane, Salome Ndjakomo
  • Atangana, Jacques

Abstract

This investigation presents the generalized cubic-quintic Guizburg-Landau (GCQGL) equation with higher-order dispersion effects in a nonlinear electrical transmission network. Based on the collective coordinates' theory with a conventional Gaussian Ansatz, the study reveals that the waves which propagate in this medium are exotic solitons such as M-shaped solitons. The investigation presents the stability of the dark soliton subjected to the quintic-phase modulation. Besides, the introduction of the cubic- and quintic-saturable nonlinearities induce the generation of twin narrow solitons, M-shaped soliton and Sasa-Satsuma soliton. Moreover, the introduction of the third-order dispersion (TOD) and the fourth-order dispersion (FOD) provokes the generation of twin large solitons associated to symmetric radiation lobes and twin narrow solitons associated to the damping effect. Some exact field solutions of the GCQGL equation are also illustrated. Moreover, some theoretical frequencies are found where significant results are exposed. In addition, physical conditions associated to the saturation lead to a particular internal perturbation. This internal excitation is measured in detail by the collective coordinates in order to build-up exotic solitons. This technique improves the comprehension of some exotic waves' mechanism of generation in nonlinear electrical transmission network.

Suggested Citation

  • Essama, Bedel Giscard Onana & Bisse, Jacquie Therese Ngo & Essiane, Salome Ndjakomo & Atangana, Jacques, 2022. "M-shaped and other exotic solitons generated by cubic-quintic saturable nonlinearities in a nonlinear electrical transmission network with higher-order dispersion effects," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005306
    DOI: 10.1016/j.chaos.2022.112320
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    References listed on IDEAS

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    1. Hanlin Chen & Zhenhui Xu & Zhengde Dai, 2014. "Rogue Wave for the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, July.
    2. Guy Roger Deffo & Serge Bruno Yamgoue & Francois Beceau Pelap, 2018. "Modulational instability and peak solitary wave in a discrete nonlinear electrical transmission line described by the modified extended nonlinear Schrödinger equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(10), pages 1-9, October.
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