IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip2s0960077921009541.html
   My bibliography  Save this article

From a generalized discrete NLS equation in discrete alpha helical proteins to the fourth-order NLS equation

Author

Listed:
  • Yang, Jun
  • Fang, Miao-Shuang
  • Luo, Lin
  • Ma, Li-Yuan

Abstract

In this paper, we consider a generalized integrable discrete nonlinear Schrödinger (NLS) equation, which can describe the dynamics of discrete alpha helical proteins with higher-order excitations and lead to the higher-order NLS equation in the continuum limit. The Darboux transformation (DT) and the soliton solutions of this generalized discrete NLS equation are implemented. It is shown that the integrable properties of the generalized discrete NLS equation, including the discrete Lax pair, the DT and the discrete soliton solutions, give rise to their continuous counterparts as the discrete space step tends to zero.

Suggested Citation

  • Yang, Jun & Fang, Miao-Shuang & Luo, Lin & Ma, Li-Yuan, 2021. "From a generalized discrete NLS equation in discrete alpha helical proteins to the fourth-order NLS equation," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009541
    DOI: 10.1016/j.chaos.2021.111600
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009541
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111600?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daniel, M. & Latha, M.M., 2001. "A generalized Davydov soliton model for energy transfer in alpha helical proteins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 351-370.
    2. Ding, Cui-Cui & Gao, Yi-Tian & Deng, Gao-Fu & Wang, Dong, 2020. "Lax pair, conservation laws, Darboux transformation, breathers and rogue waves for the coupled nonautonomous nonlinear Schrödinger system in an inhomogeneous plasma," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    3. Hai-Qiang Zhang & Bo Tian & Xiang-Hua Meng & Xing Lü & Wen-Jun Liu, 2009. "Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(2), pages 233-239, November.
    4. Eskandar, S. & Hoseini, S.M., 2018. "Soliton solutions and eigenfunctions of linearized operator for a higher-order nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 289-294.
    5. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
    6. Saravana Veni, S. & Latha, M.M., 2014. "Nonlinear excitations in a disordered alpha-helical protein chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 76-85.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Muniyappan, A. & Parasuraman, E. & Kavitha, L., 2023. "Stability analysis and discrete breather dynamics in the microtubulin lattices," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Yu & Li, Chuanzhong & He, Jingsong, 2016. "Rogue waves in a resonant erbium-doped fiber system with higher-order effects," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 826-841.
    2. Du, Zhong & Meng, Gao-Qing & Du, Xia-Xia, 2021. "Localized waves and breather-to-soliton conversions of the coupled Fokas–Lenells system," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Zhong, WenYe & Qin, Pei & Zhong, Wei-Ping & Belić, Milivoj, 2022. "Two-dimensional rogue wave clusters in self-focusing Kerr-media," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Lou, Yu & Zhang, Yi, 2022. "Breathers on elliptic function background for a generalized nonlinear Schrödinger equation with higher-order terms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 22-31.
    5. Li, Liu-Qing & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui & Wang, Dong, 2022. "Bilinear form and nonlinear waves of a (1+1)-dimensional generalized Boussinesq equation for the gravity waves over water surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 494-508.
    6. Vakhnenko, Oleksiy O. & Vakhnenko, Vyacheslav O. & Verchenko, Andriy P., 2023. "Dipole–monopole alternative as the precursor of pseudo-excitonic chargeless half-mode in an integrable nonlinear exciton–phonon system on a regular one-dimensional lattice," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Jin, Xin-Wei & Zhao, Yi-Miao & Duan, Liang & Yang, Zhan-Ying & Yang, Wen-Li, 2024. "Voltage manipulation of magnetic rogue waves for controllable electromagnetic interference," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    8. Seadawy, Aly R. & Ali, Safdar & Rizvi, Syed T.R., 2022. "On modulation instability analysis and rogue waves in the presence of external potential: The (n + 1)-dimensional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    9. Durairaj, Premraj & Premalatha, K. & Kanagaraj, Sathiyadevi & Zheng, Zhigang & Rajagopal, Karthikeyan, 2024. "Emergence of nonchaotic bursting extreme events in a quadratic jerk oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    10. Chen, Su-Su & Tian, Bo & Qu, Qi-Xing & Li, He & Sun, Yan & Du, Xia-Xia, 2021. "Alfvén solitons and generalized Darboux transformation for a variable-coefficient derivative nonlinear Schrödinger equation in an inhomogeneous plasma," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    11. Yassine Benia & Marianna Ruggieri & Andrea Scapellato, 2019. "Exact Solutions for a Modified Schrödinger Equation," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    12. Miguel Onorato & Pierre Suret, 2016. "Twenty years of progresses in oceanic rogue waves: the role played by weakly nonlinear models," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(2), pages 541-548, November.
    13. Li, Wentao & Li, Biao, 2024. "Construction of degenerate lump solutions for (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    14. Xianguo Geng & Ruomeng Li, 2019. "On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation," Mathematics, MDPI, vol. 7(10), pages 1-23, October.
    15. Xi-zhong Liu & Zhi-Mei Lou & Xian-Min Qian & Lamine Thiam, 2019. "A Study on Lump and Interaction Solutions to a (3 + 1)-Dimensional Soliton Equation," Complexity, Hindawi, vol. 2019, pages 1-12, October.
    16. Sang, Xue & Dong, Huanhe & Fang, Yong & Liu, Mingshuo & Kong, Yuan, 2024. "Soliton, breather and rogue wave solutions of the nonlinear Schrödinger equation via Darboux transformation on a time–space scale," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    17. Li, Min & Wang, Boting & Xu, Tao & Wang, Lei, 2021. "Quantitative analysis on the bifurcations and exact travelling wave solutions of a generalized fourth-order dispersive nonlinear Schrödinger equation in Heisenberg spin chain," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    18. Li, Lingfei & Yan, Yongsheng & Xie, Yingying, 2022. "Rational solutions with non-zero offset parameters for an extended (3 + 1)-dimensional BKP-Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    19. Alexandra Völkel & Luca Nimmesgern & Adam Mielnik-Pyszczorski & Timo Wirth & Georg Herink, 2022. "Intracavity Raman scattering couples soliton molecules with terahertz phonons," Nature Communications, Nature, vol. 13(1), pages 1-6, December.
    20. Zhang, Xi & Wang, Yu-Feng & Yang, Sheng-Xiong, 2024. "Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009541. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.