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On PT symmetry systems: invariance, conservation laws, and reductions. (English) Zbl 1442.35427

Summary: 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.”

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35B06 Symmetries, invariants, etc. in context of PDEs
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