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On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions

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  • P. Masemola
  • A. H. Kara

Abstract

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.”

Suggested Citation

  • P. Masemola & A. H. Kara, 2014. "On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, August.
    • Handle: RePEc:hin:jnljam:849361
    DOI: 10.1155/2014/849361
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