Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1873-1885.

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Soliton Solutions and Its Nonlinear Dynamics Behavior Research of the Three-Component Four-Order Nonlinear Schrödinger System in Alpha Helical Protein

Liu Jiayu1, Wei Hanyu2, Zhang Yan2, Xia Tiecheng3, Wang Hui4   

  1. 1. Department of Basic Sciences, Henan College of Transportation, Zhengzhou 450005;
    2. College of Mathematics and Statistics, Zhoukou Normal University, Henan Zhoukou 466001;
    3. Department of Mathematics, Shanghai University, Shanghai 200444;
    4. College of Art and Sciences, Shanghai Maritime University, Shanghai 201306
  • Received:2021-10-26 Revised:2022-07-01 Published:2022-12-16
  • Supported by:
    Supported by the NSFC(12026245, 11975145, 11905124), the Natural Science Foundation of Henan (202300410524), the Program for Science \& Technology Innovation Talents in Universities of Henan Province(22HASTIT019) and the Academic Degrees \& Graduate Education Reform Project of Henan Province(2021SJGLX219Y)

Abstract: Complexes of proteins are central to certain cellular processes, investigated in this paper is the three-component fourth-order nonlinear Schrödinger system, which is used for describing the alpha helical proteins with interspine coupling. First, the matrix Rieman-Hilbert problem for the system is derived by scattering and inverse-scattering transformations through the Rieman-Hilbert method. Then, a unique solution is constructed by using discrete scattering data from the Rieman-Hilbert problem under the reflectionless. Furthermore, the $N$-soliton solution formula of three-component fourth-order nonlinear Schrödinger system is obtained with the help of potential reconstruction. In the case of $N= 1,2,3$, the explicit expressions of soliton solutions, breather solutions and interaction solutions are formulated by means of Maple symbolic computation. Finally, the propagation and collision dynamic behaviors as well as localized wave characteristics of these solutions are further analyzed by selecting appropriate parameters with some graphics. The results show that the higher-order linear and nonlinear term coefficient $\gamma$ has important impact on the velocity, phase, period, and wavewidth of wave dynamics. Meanwhile, collisions for the high-order breathers and muli-soliton solutions are elastic interaction which imply they remain bounded all the time.

Key words: Riemann-Hilbert approach, Spectral analysis, Three-component four-order nonlinear Schrödinger system, Breathers

CLC Number: 

  • O175.24