On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions - P. Masemola; A. H. Kara (Journal of Applied Mathematics)
An analysis of a PT symmetric coupler with “gain in one waveguide and loss in another” is made; a transformation in the PT system and some assumptions results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”