1204.0768 (Robert L. Anderson)

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

Robert L. Anderson

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 $n=1$.

View original: http://arxiv.org/abs/1204.0768