The short pulse equation is integrable

Details The short pulse equation is integrable The short pulse equation is integrable

2004-09-19

arxiv.org/abs/nlin/0409034v1

J. Phys. Soc. Jpn. 74 (2005) 239-241

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages

Scientific paper

10.1143/JPSJ.74.239

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.

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