论文标题
等法$ n $二维非线性PDM振荡器：线性化，不变性和精确的溶解度
Isochronous $n$-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability
论文作者
论文摘要
在标准的Lagrangian设置（即动力学和势能之间的差异）中，我们讨论和报告了一些$ n $二维的非线性位置依赖性质量（PDM）振荡器的等视性，线性化性和确切的溶解度。在此过程中，负面的PDM功能力场的梯度不再与规范动量的时间导数有关，$ \ Mathbf {p}％= m \ m \ left（r \右）\ Mathbf {\ dot {\ dot {r}} $，但与Pse derivative of Pse derivative of psse derivative of pseudo-moment of pseument-moment of psse derivative-moment of。 $ \ mathbf {π} \ left（r \ right）= \ sqrt {％m \ left（r \ right）} \ mathbf {\ dot {r}} $（即，noethermoment）。此外，使用某个点转换配方，我们表明$ n $二维非线性PDM振荡器的线性化性仅适用于$ n = 1 $，但对于$ n \ geq 2 $才有可能。在PDM设置下，Euler-Lagrange不变性在$ n \ geq 2 $中跌落/不完整。因此，寻求替代性不向导。这样的不变，例如Mustafa \ cite {42}的\ emph {Newtonian不变性}，有效地授权使用一个系统的确切解决方案来找到另一个系统的解决方案。报道了等于$ n $ n $二维的非线性PDM振荡器的样本示例。
Within the standard Lagrangian settings (i.e., the difference between kinetic and potential energies), we discuss and report isochronicity, linearizability and exact solubility of some $n$-dimensional nonlinear position-dependent mass (PDM) oscillators. In the process, negative the gradient of the PDM-potential force field is shown to be no longer related to the time derivative of the canonical momentum, $\mathbf{p}% =m\left( r\right) \mathbf{\dot{r}}$, but it is rather related to the time derivative of the pseudo-momentum, $\mathbf{π}\left( r\right) =\sqrt{% m\left( r\right) }\mathbf{\dot{r}}$ (i.e., Noether momentum). Moreover, using some point transformation recipe, we show that the linearizability of the $n$-dimensional nonlinear PDM-oscillators is only possible for $n=1$ but not for $n\geq 2$. The Euler-Lagrange invariance falls short/incomplete for $n\geq 2$ under PDM settings. Alternative invariances are sought, therefore. Such invariances, like \emph{Newtonian invariance} of Mustafa \cite{42}, effectively authorize the use of the exact solutions of one system to find the solutions of the other. A sample of isochronous $n$-dimensional nonlinear PDM-oscillators examples are reported.
