The short pulse equation is integrable
Exactly Solvable and Integrable Systems
2007-05-23 v1 Mathematical Physics
Analysis of PDEs
math.MP
Optics
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.
Cite
@article{arxiv.nlin/0409034,
title = {The short pulse equation is integrable},
author = {Anton Sakovich and Sergei Sakovich},
journal= {arXiv preprint arXiv:nlin/0409034},
year = {2007}
}
Comments
7 pages