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In this paper, we present an explicit form in terms of end-point data for theclassical action $S_{2n}$ evaluated on extremals satisfying the Hamilton-Jacobiequation for each member of a hierarchy of classical non-relativisticoscillators 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 nonlinearquartic oscillator corresponds to $n=2$ while the harmonic oscillatorcorresponds to $n=1$.

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