Actions for an Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1+1 Dimensions

Details Actions for an Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1+1 Dimensions Actions for an Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1+1 Dimensions

2012-04-03

arxiv.org/abs/1204.0768v1

Physics

Mathematical Physics

Scientific paper

In this paper, we present an explicit form in terms of end-point data for the classical action $S_{2n}$ evaluated on extremals satisfying the Hamilton-Jacobi equation for each member of a hierarchy of classical non-relativistic oscillators characterized by even power potentials (i.e., attractive potentials $V_{2n}(y_{2n})={\frac{1}{2n}}k_{2n}y_{2n}^{2n}(t)|_{n{\geq}1}$). The nonlinear quartic oscillator corresponds to $n=2$ while the harmonic oscillator corresponds to $n=1$.

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