α-螺旋蛋白中三分量高阶非线性薛定谔方程的怪波解  

Rogue wave solutions of the three-component high-order nonlinear Schrödinger equation in α-helix protein

作　　者：王梦雅 陈婷婷[1] 王立洪[1] WANG Mengya;CHEN Tingting;WANG Lihong(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2024年第1期20-30,共11页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：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)。

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.The three-component higher-order nonlinear Schrödinger 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.

关 键 词：三分量高阶非线性薛定谔方程 LAX对 达布变换 怪波 

分 类 号：O175.29[理学—数学]