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The short pulse equation is integrable

Anton Sakovich·Sergei Sakovich
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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.

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Anton Sakovich, Sergei Sakovich. 2004-09-19. The short pulse equation is integrable. https://doi.org/10.1143/jpsj.74.239

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