离散非线性薛定谔方程的1∶1共振  

1∶1 Resonance of Discrete Nonlinear Schr dinger Equation

作　　者：张文娴 邓圣福 ZHANG Wenxian;DENG Shengfu(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2023年第4期526-532,共7页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金面上资助项目(12171171)。

摘　　要：为研究离散非线性薛定谔方程在不动点附近的1∶1共振问题,将离散非线性薛定谔方程化为差分系统,差分系统线性算子的特征值为两重根1;然后,利用Picard迭代及时间1映射,将差分系统转换为常微分系统,推导差分系统不动点的稳定性;最后,用数学软件模拟差分系统的局部相图.研究结果表明:不动点是局部渐近稳定的.In order to study 1∶1 resonance problem of discrete nonlinear Schr dinger equation near the fixed point,firstly,this discrete nonlinear Schr dinger equation is transformed into a difference system,the eigenvalue of the difference system linear operator is double root 1,and then,by the use of Picard iteration and the time-one map,this difference system is converted into an ordinary differential system,the stability of the fixed point of the difference system is obtained.Lastly,the local phase portraits of the difference system are also simulated by mathematical software.The result shows that the fixed point is locally asymptotically stable.

关 键 词：离散非线性薛定谔方程 差分系统 1∶1共振 Picard迭代 退化平衡点 多项式函数 

分 类 号：O175.1[理学—数学]