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

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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).
    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.
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    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).

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