阿尔法螺旋蛋白中三分量四阶非线性Schrödinger系统孤子解及其非线性动力行为研究

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1873-1885.

阿尔法螺旋蛋白中三分量四阶非线性Schrödinger系统孤子解及其非线性动力行为研究

刘甲玉¹,魏含玉^2,*(),张燕²,夏铁成³,王惠⁴

¹ 河南交通职业技术学院基础教学部郑州 450005
² 周口师范学院数学与统计学院河南周口 466001
³ 上海大学数学系上海 200444
⁴ 上海海事大学文理学院上海 201306

收稿日期:2021-10-26 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 魏含玉 E-mail:weihanyu8207@163.com
基金资助:
国家自然科学基金(12026245);国家自然科学基金(11975145);国家自然科学基金(11905124);河南省自然科学基金(202300410524);河南省高校科技创新人才支持计划(22HASTIT019);河南省高等教育教学改革研究与实践项目(学位与研究生教育)(2021SJGLX219Y)

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

Jiayu Liu¹,Hanyu Wei^2,*(),Yan Zhang²,Tiecheng Xia³,Hui Wang⁴

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 Online:2022-12-26 Published:2022-12-16
Contact: Hanyu Wei E-mail:weihanyu8207@163.com
Supported by:
the NSFC(12026245);the NSFC(11975145);the NSFC(11905124);the Natural Science Foundation of Henan(202300410524);the Program for Science & Technology Innovation Talents in Universities of Henan Province(22HASTIT019);the Academic Degrees & Graduate Education Reform Project of Henan Province(2021SJGLX219Y)

摘要/Abstract

摘要：

蛋白质复合体是某些细胞过程的中心, 该文研究了三分量四阶非线性Schrödinger系统, 可以用于描述具有脊间耦合的四阶阿尔法螺旋蛋白.首先利用黎曼-希尔伯特方法, 对相关谱问题进行散射和反散射变换, 严格推导出该系统的矩阵黎曼-希尔伯特问题.其次从无反射情况下的黎曼-希尔伯特问题出发, 利用离散散射数据构造出黎曼-希尔伯特问题的唯一解.进一步通过位势重构, 得到三分量四阶非线性Schrödinger系统的$N$孤子解公式.在$N=1, 2, 3$的情况下, 利用Maple符号计算, 得到孤子解、呼吸解和相互作用解的精确显式表达式.最后通过选择合适的参数, 用一些图形进一步分析了这些解的传播和碰撞动力学行为以及局部波结构.结果表明, 高阶线性和非线性项系数$\gamma$对波动力学的速度、相位、周期和波宽都有重要影响.同时, 高阶呼吸子解和多孤子解的碰撞是弹性相互作用, 这意味着它们始终是有界的.

关键词: 黎曼-希尔伯特方法, 谱分析, 三分量四阶非线性Schrödinger系统, 呼吸解

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

中图分类号:

O175.24

刘甲玉,魏含玉,张燕,夏铁成,王惠. 阿尔法螺旋蛋白中三分量四阶非线性Schrödinger系统孤子解及其非线性动力行为研究[J]. 数学物理学报, 2022, 42(6): 1873-1885.

Jiayu Liu,Hanyu Wei,Yan Zhang,Tiecheng Xia,Hui Wang. Soliton Solutions and Its Nonlinear Dynamics Behavior Research of the Three-Component Four-Order Nonlinear Schrödinger System in Alpha Helical Protein[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1873-1885.

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