## Symmetries of the Hamilton–Jacobi equation

##### Citation

Boyer, C.P. & Kalnins, E.G. (1977). Symmetries of the Hamilton–Jacobi equation. Journal of Mathematical Physics, 18, 1032.

Permanent Research Commons link: http://hdl.handle.net/10289/1234

##### Abstract

We present a detailed discussion of the infinit esimal symmetries of the Hamilton-Jacobi equation (an arbitrary first order partial equation) Our presentation clucidates the role played by the characteristic system in determining the symmetries. We then specialize to the case of a free particle in one space and one time dimension, and study of local Lie group of point transformations locally isomorphie to O(3,2). We show that the separation of variables of the corresponding Hamilton-Jacobi equation n the form of a sum is related to orbits in the Schrödinger subalgebra of c(3,2). The remaining orbits of o(3,2) yield symmetry related solutions which separate in more complicated product forms. Finally some connections with the primordial equation of hydrodynamics (without force terms) are made.

##### Date

1977-05##### Type

##### Rights

Copyright 1977 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp