α-螺旋蛋白中三分量高阶非线性薛定谔方程的怪波解
PDF下载 (143)王梦雅,陈婷婷,王立洪.α-螺旋蛋白中三分量高阶非线性薛定谔方程的怪波解[J].宁波大学学报(理工版),2024,37(1):20-30.DOI:10.20098/j.cnki.1001-5132.2023.0718
WANG Mengya,CHEN Tingting,WANG Lihong.Rogue wave solutions of the three-component high-order nonlinear Schr?dinger equation in α-helix protein[J].Journal of Ningbo University(Natural Science & Engineering Edition),2024,37(1):20-30.DOI:10.20098/j.cnki.1001-5132.2023.0718
| Title: | Rogue wave solutions of the three-component high-order nonlinear Schr?dinger equation in α-helix protein |
| 作者: | 王梦雅, 陈婷婷, 王立洪 |
| Author(s): | WANG Mengya, CHEN Tingting, WANG Lihong |
| 关键词: | 三分量高阶非线性薛定谔方程; Lax对; 达布变换; 怪波 |
| Keywords: | three-component higher-order nonlinear Schr?dinger equation; Lax pair; Darboux transformation; rogue wave |
| 分类号: | O175.29 |
| DOI: | 10.20098/j.cnki.1001-5132.2023.0718 |
| 文献标识码: | A |
| 摘要: | 以三分量高阶非线性薛定谔方程为α-螺旋蛋白中生物能量沿蛋白质分子链传输的控制方程, 研究三个相互耦合的波函数在极限状态下激发的怪波. 基于控制模型的Lax对表示, 利用规范变换得到了达布变换的行列式形式. 通过Lax对的变量分离和平移参数的引入, 给出了怪波激发的代数条件. 进一步利用幂级数的多项分裂构造怪波解的基础特征函数, 并由此导出退化的达布变换. 最后通过退化的达布变换获得怪波解, 并在不同参数下, 用三维图形示例怪波的波形演化及其极值轨迹. |
| Abstract: | The three-component higher-order nonlinear Schr?dinger equation is used as the governing equation for the propagation of biological energy along the molecular chain of alpha helical proteins with interspine coupling at higher order, and the rogue waves excited by three coupled wave functions in the limit state are investigated. Based on the Lax pair representation of the governing model, the determinant form of the Darboux transformation is derived using the gauge transformation. Through the variables separation of Lax pair and the introduction of translation parameters, the algebraic conditions for the excitation of rogue wave are given. Furthermore, the fundamental characteristic functions of the rogue wave solution are constructed with the multisection of power series, with the use of which the degenerated Darboux transformation is derived. Finally, the rogue wave solutions are obtained using degenerated Darboux transformation and the waveform evolution, and extreme value trajectory of rogue waves are illustrated with three-dimensional figures under different parameters. |
| 参考文献 /References: | [1] DAVYDOV A S. The theory of contraction of proteins under their excitation[J]. Journal of Theoretical Biology, 1973, 38(3):559-569. [2] DAVYDOV A S. Solitons in molecular systems[M]. Dordrecht: Springer Netherlands, 1985. [3] SOLOVYEV V V, SALAMOV A A. Predicting α-helix and β-strand segments of globular proteins[J]. Bioinformatics, 1994, 10(6):661-669. [4] CHENG W, YAN C H. Detecting periodicity associated with the alpha-helix structure using Fourier transform[J]. Computational Molecular Bioscience, 2012, 2(4):109-114. [5] PENG X B, LIU J J, DAI J, et al. Application of topological soliton in modeling protein folding: Recent progress and perspective[J]. Chinese Physics B, 2020, 29(10):108705. [6] PANG X F. The biological effect and medical functions of the infrared rays[J]. Chinese Journal of Biomedical Engineering (English Edition), 2001, 10(1):27-37. [7] DANIEL M, LATHA M M. Soliton in discrete and continuum alpha helical proteins with interspine coupling[J]. Physics Letters A, 1999, 252(1/2):92-108. [8] DANIEL M, DEEPAMALA K. Davydov soliton in alpha helical proteins: higher order and discreteness effects[J]. Physica A: Statistical Mechanics and its Applications, 1995, 221(1/2/3):241-255. [9] DANIEL M, LATHA M M. A generalized Davydov soliton model for energy transfer in alpha helical proteins[J]. Physica A: Statistical Mechanics and its Applications, 2001, 298(3/4):351-370. [10] SCOTT A. Davydov’s soliton[J]. Physics Reports, 1992, 217(1):1-67. [11] PANG X F. Improvement of the Davydov theory of bioenergy transport in protein molecular systems[J]. Physical Review E, 2000, 62(5):6989-6998. [12] BRIZHIK L, EREMKO A, PIETTE B, et al. Solitons in α-helical proteins[J]. Physical Review E, 2004, 70(3):031914. [13] D’OVIDIO F, BOHR H G, LINDG?RD P A. Solitons on H-bonds in proteins[J]. Journal of Physics: Condensed Matter, 2003, 15(18):S1699-S1707. [14] WANG X M, LI P F. Breathers and solitons for the coupled nonlinear Schr?dinger system in three-spine α-helical protein[J]. Chinese Physics B, 2021, 30(10):100509. [15] CHAN H N, CHOW K W. Rogue wave modes for the coupled nonlinear Schr?dinger system with three components: a computational study[J]. Applied Sciences, 2017, 7(6):559. [16] DANIEL M, LATHA M M. Soliton in alpha helical proteins with interspine coupling at higher order[J]. Physics Letters A, 2002, 302(2/3):94-104. [17] L? X, LIN F H. Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order[J]. Communications in Nonlinear Science and Numerical Simulation, 2016, 32:241-261. [18] WRIGHT O C. The Darboux transformation of some Manakov systems[J]. Applied Mathematics Letters, 2003, 16(5):647-652. [19] 李翊神. 规范变换, 贝克隆变换与非线性叠加公式[J]. 数学进展, 1989, 18(3):356-372. [20] 贺劲松, 张玲, 程艺, 等. AKNS系统Darboux变换的行列式表示[J]. 中国科学(数学), 2006, 36(9):971-983. [21] GUO L J, WANG L H, CHENG Y, et al. Higher-order rogue waves and modulation instability of the two-component derivative nonlinear Schr?dinger equation[J]. Communications in Nonlinear Science and Numerical Simulation, 2019, 79:104915. [22] PEREGRINE D H. Water waves, nonlinear Schr?dinger equations and their solutions[J]. Journal of the Australian Mathematical Society Series B, 1983, 25(1):16-43. [23] WANG L H, HE J S, XU H, et al. Generation of higher-order rogue waves from multibreathers by double degeneracy in an optical fiber[J]. Physical Review E, 2017, 95(4):042217. |
| 备注/Memo: | 收稿日期: 2023－07－25. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（12071304）; 浙江省大学生科技创新活动计划（新苗人才计划）（2021R405089）. 第一作者: 王梦雅, 硕士研究生, 主要研究方向: 孤立子与可积方程. E-mail: wangmengya1998s@163.com *通信作者: 王立洪, 副教授, 主要研究方向: 孤立子与可积方程. E-mail: wanglihong@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
