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• W3131508712 abstract "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, $mathbf{p}% =mleft( rright) mathbf{dot{r}}$, but it is rather related to the time derivative of the pseudo-momentum, $mathbf{pi }left( rright) =sqrt{% mleft( rright) }mathbf{dot{r}}$ (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 $ngeq 2$. The Euler-Lagrange invariance falls short/incomplete for $ngeq 2$ 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." @default.
• W3131508712 created "2021-03-01" @default.
• W3131508712 creator A5024938434 @default.
• W3131508712 date "2021-02-01" @default.
• W3131508712 modified "2023-09-30" @default.
• W3131508712 title "Isochronous n-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability" @default.
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• W3131508712 doi "https://doi.org/10.1140/epjp/s13360-021-01250-0" @default.
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