Integrability in theories with local U(1) gauge symmetry

@article{Adam2007IntegrabilityIT,
  title={Integrability in theories with local U(1) gauge symmetry},
  author={Christoph Adam and Joaquin Sanchez-Guillen and Andrzej Wereszczynski},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2007},
  volume={40},
  pages={9079 - 9088}
}
Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1… 

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