Two-dimensional Systems that Arise from the Noether Classification of Lagrangians on the Line

摘要: The Noether-like operators that play an essential role in writing down the invariants for systems of two ordinary differential equations (ODEs) are constructed. classification such is carried out with help analytic continuation Lagrangians on line. Cases which also Noether symmetries ODEs briefly mentioned. In particular, 8-dimensional maximal subalgebra remarkabely obtained simplest system free particle dimensions from 5-dimensional complex algebra. We present effectivness as well determination all first integrals nonlinear equation have not been reported before. This study gives a new direction to construct equations.