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The short pulse equation is integrable

By Anton Sakovich and Sergei Sakovich

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.Comment: 7 page

Topics: Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, Mathematics - Analysis of PDEs, Physics - Optics
Publisher: 'Japan Society of Applied Physics'
Year: 2004
DOI identifier: 10.1143/JPSJ.74.239
OAI identifier: oai:arXiv.org:nlin/0409034

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