On elliptic string solutions in AdS3 and dS3

@article{Bakas2016OnES,
  title={On elliptic string solutions in AdS3 and dS3},
  author={Ioannis Bakas and Georgios Pastras},
  journal={Journal of High Energy Physics},
  year={2016},
  volume={2016},
  pages={1-53}
}
A bstractClassical string actions in AdS3 and dS3 can be connected to the sinh-Gordon and cosh-Gordon equations through Pohlmeyer reduction. We show that the problem of constructing a classical string solution with a given static or translationally invariant Pohlmeyer counterpart is equivalent to solving four pairs of effective Schrödinger problems. Each pair consists of a flat potential and an n = 1 Lamé potential whose eigenvalues are connected, and, additionally, the four solutions satisfy a… 

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