Lie analysis is a systematic procedure for identifying continuous symmetries of an equation. If the equation possesses continuous symmetries, we may be able to find related conservation laws. Some equations possess multiple symmetries and conservation laws while other equations do not contain any symmetries or conservation laws. Using this procedure with a known generalized path, we may be able to derive conserved quantities even if we do not know how to choose the generalized potential at first. Some systems might even contain multiple conserved quantities, and this procedure will give us a complete set of conserved quantities.
- 14.2: Types of Symmetries
- This chapter is concerned with identifying symmetries of equations. We say that an equation contains a symmetry if the solution to the equation is the same both before and after a symmetry transformation is applied.