The short pulse equation is integrable

@inproceedings{Sakovich2008TheSP,
  title={The short pulse equation is integrable},
  author={Anton Sakovich and Sergei Sakovich},
  year={2008}
}
We prove that the Schäfer–Wayne short pulse equation (SPE) which describes the propagation of ultra-short optical pulses in nonlinear media is integrable. First, we discover a Lax pair of the SPE which turns out to be of the Wadati–Konno–Ichikawa type. Second, we construct a chain of transformations which relates the SPE with the sine-Gordon equation. 

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