Integration of the Classical Action for the Quartic Oscillator in 1 + 1 Dimensions

DOI: 10.4236/am.2013.410A3014   PDF   HTML   XML   4,764 Downloads   6,215 Views   Citations

Abstract

In this paper, we derive an explicit form in terms of end-point data in space-time for the classical action, i.e. integration of the Lagrangian along an extremal, for the nonlinear quartic oscillator evaluated on extremals.

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R. Anderson, "Integration of the Classical Action for the Quartic Oscillator in 1 + 1 Dimensions," Applied Mathematics, Vol. 4 No. 10C, 2013, pp. 117-122. doi: 10.4236/am.2013.410A3014.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] H. Goldstein, “Classical Mechanics,” Addison-Wesley Publishing Company, Reading, 1980.
[2] R. L. Anderson, “An Invertible Linearization Map for the Quartic Oscillator,” Journal of Mathematical Physics, Vol. 51, No. 12, 2010, Article ID: 122904.
[3] R. C. Santos, J. Santos and J. A. S. Lima, “HamiltonJacobi Approach for Power-Law Potentials,” Brazilian Journal of Physics, Vol. 36, No. 4A, 2006, pp. 12571261.
[4] R. L. Anderson, “Actions for a Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1 + 1 Dimensions,” arXiv.org:1204.0768.

  
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