The Short Pulse Equation Is Integrable
Abstract
We prove that the SchäferWayne short pulse equation (SPE), which describes the propagation of ultrashort optical pulses in nonlinear media, is integrable. First, we discover a Lax pair of the SPE that is found to be of the WadatiKonnoIchikawa type. Second, we construct a chain of transformations that relates the SPE with the sineGordon equation.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 January 2005
 DOI:
 10.1143/JPSJ.74.239
 arXiv:
 arXiv:nlin/0409034
 Bibcode:
 2005JPSJ...74..239S
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  Mathematical Physics;
 Physics  Optics
 EPrint:
 7 pages