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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. 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).
    2. Gang Xu & Alexander U. Nielsen & Bruno Garbin & Lewis Hill & Gian-Luca Oppo & Julien Fatome & Stuart G. Murdoch & Stéphane Coen & Miro Erkintalo, 2021. "Spontaneous symmetry breaking of dissipative optical solitons in a two-component Kerr resonator," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
    3. 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.
    4. Samad Noeiaghdam & Denis Sidorov & Abdul-Majid Wazwaz & Nikolai Sidorov & Valery Sizikov, 2021. "The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    5. Kumar, Sachin & Kumar, Dharmendra & Kumar, Amit, 2021. "Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
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    1. Cao, Na & Yin, XiaoJun & Bai, ShuTing & LiYangXu,, 2023. "Breather wave, lump type and interaction solutions for a high dimensional evolution model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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