The potential function problem for the Klein-Gordon equation. (English) Zbl 1498.37116
Summary: Several spaces which are decomposable are investigated in relation to the collineations and Lie symmetries of the Klein-Gordon equations. Nine classes of solutions are presented, including their conformal vectors. Some of the spaces represent perfect fluids or vacuum spaces. For each vector field, explicit expressions are obtained to define the potential function embedded into the Klein-Gordon equation.
MSC:
| 37L20 | Symmetries of infinite-dimensional dissipative dynamical systems |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35Q51 | Soliton equations |
| 35C05 | Solutions to PDEs in closed form |
| 70G65 | Symmetries, Lie group and Lie algebra methods for problems in mechanics |
Keywords:
Klein-Gordon equation; conformal vectors; potential functions; reducible spaces; vector fieldsReferences:
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