Noether-Type Conserved Quantities on Time Scales for Birkhoffian Systems with Delayed Arguments
Noether-Type Conserved Quantities on Time Scales for Birkhoffian Systems with Delayed Arguments
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DOI：
10.1007/s40010-021-00741-0
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
X. Zhai;Yi Zhang
中科院分区：
文献类型：
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作者：
X. Zhai;Yi Zhang
本文讨论了时标形式下具有时滞变元的Birkhoff系统的Noether对称性和守恒量。首先建立了变量定义在时标上的时滞变元Pfaff-Birkhoff原理，并由此导出了时标上相应的时滞Birkhoff方程。其次，分析了时标上具有时滞变元的Pfaff作用在单参数群的无穷小变换下的不变性。进一步，利用时间重参数化技术和延迟变元线性变换，证明了系统的Noether定理，揭示了对称性与守恒量之间的关系.最后，将经典的Noether型守恒量、离散的Noether型守恒量和量子的Noether型守恒量结合起来。最后通过一个例子说明了结果的应用。
This paper deals with the Noether symmetry and conserved quantity for Birkhoffian system with delayed arguments in version of time scales. Firstly, the Pfaff–Birkhoff principle with delayed arguments in which the variables are defined on time scales is established, through which the corresponding time-delayed Birkhoff’s equations on time scales are derived. Secondly, the invariance of the Pfaff action with delayed arguments on time scales under the infinitesimal transformations of one-parameter group is analyzed. Further, the Noether theorem for the system which reveals the relationship between the symmetry and conserved quantity is proved by applying a technique of time reparameterization and performing the linear change of the variables with delayed arguments. Finally, the results incorporate the classical Noether-type conserved quantity, the discrete Noether-type conserved quantity and the quantum Noether-type conserved quantity. Also, an example illustrates the application of the results.