Symmetry and Integrability of Equations of Mathematical Physics − 2018

Stanislav Opanasenko (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine; Memorial University of Newfoundland, St. John’s, Canada)
Roman Popovych (Silesian University in Opava, Czechia; University of Vienna, Austria; Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

Generalized symmetries and conservation laws of (1+1)-dimensional Klein−Gordon equation

Abstract:
We explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein−Gordon equation. This allows us to describe this algebra in terms of the universal enveloping algebra of the essential Lie invariance algebra of the Klein−Gordon equation. Then we single out variational symmetries of the corresponding Lagrangian and compute the space of local conservation laws of this equation.

[1] Opanasenko S. and Popovych R.O., Generalized symmetries and conservation laws of (1+1)-dimensional Klein−Gordon equation, arXiv:1810.12434, 13 pp.