• 论文 •

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

1. 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 修回日期:2022-07-01 发布日期:2022-12-16
• 通讯作者: 魏含玉,E-mail:weihanyu8207@163.com E-mail:weihanyu8207@163.com
• 基金资助:
国家自然科学基金(12026245,11975145,11905124)、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)和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

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
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.