The short pulse equation is integrable
arXiv:nlin/0409034 · doi:10.1143/JPSJ.74.239
Abstract
We prove that the Schafer-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.
7 pages