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Multiple lump, generalized breathers, Akhmediev breather, manifold periodic and rogue wave solutions for generalized Fitzhugh-Nagumo equation: Applications in nuclear reactor theory

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  • Seadawy, Aly R.
  • Rizvi, Syed T.R.
  • Ahmed, Sarfaraz

Abstract

Based on ansatz functions technique, we construct many types of novel wave structures and multiple lump-soliton solutions to the generalized Fitzhugh-Nagumo (gFN)-equation. In particular, we obtain entirely exciting lump, lump 1-kink, lump 2-kink, lump-periodic, manifold periodic-soliton, periodic cross-rational, kink cross-rational (KCR) solutions, interaction of the multi-lump and periodic solutions as well as breather style of solitary wave solutions. Using a transformation of dependent variable, which contain a controlling parameter (can control the direction, wave height and angle of the traveling wave), we build generalized breathers, rogue wave, Akhmediev breather, homoclinic breather, Ma breather, Kuznetsov-Ma breather and their relating rogue waves, multiwave, M-shaped rational and some various interactions. We show the results of our solutions graphically in distinct dimensions by assigning different values to the parameters.

Suggested Citation

  • Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz, 2022. "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, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005367
    DOI: 10.1016/j.chaos.2022.112326
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    References listed on IDEAS

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    1. Mengjie Yu & Jae K. Jang & Yoshitomo Okawachi & Austin G. Griffith & Kevin Luke & Steven A. Miller & Xingchen Ji & Michal Lipson & Alexander L. Gaeta, 2017. "Breather soliton dynamics in microresonators," Nature Communications, Nature, vol. 8(1), pages 1-7, April.
    2. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz, 2022. "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, Elsevier, vol. 160(C).
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    2. Rafiq, Muhammad Naveed & Chen, Haibo, 2024. "Dynamics of three-wave solitons and other localized wave solutions to a new generalized (3+1)-dimensional P-type equation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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