The Short Pulse Equation Is Integrable
By Anton Sakovich, Sergei Sakovich. 2004
287 citations recorded by the source corpus.
We prove that the Schafer–Wayne 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 Wadati–Konno–Ichikawa type. Second, we construct a chain of transformations that relates the SPE with the sine-Gordon equation.
Subfields: Spectroscopy, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/4050ab2a89d5bade573921d47bbd5b87ff4a278b
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In Spectroscopy
In Statistical and Nonlinear Physics
- B. Feng
- Zuo-nong Zhu
- Liming Ling
- Nail H. Ibragimov
- Panayotis G. Kevrekidis
- Atanas Stefanov
- Anton Sakovich
- Yannan Shen
Citations in the corpus
- Multi-soliton, multi-breather and higher order rogue wave solutions to the complex short pulse equation (2015, methodology): “The connection between the SP equation (1) and the sine-Gordon equation through the reciprocal transformation was firstly discovered in [19], then was further clarified and used to find two-loop and breather solutions in [22] by the same authors.”
- Nonlinear self-adjointness in constructing conservation laws (2011, background): “1) by a non-point transformation which is constructed in [32] as a chain of differential substitutions (given also in [31] by Eqs.”
- From the Real and Complex Coupled Dispersionless Equations to the Real and Complex Short Pulse Equations (2016, unknown): “which coincides with the Lax pair of the SP equation obtained in [18, 33].”
- Complex short pulse and coupled complex short pulse equations (2013, background): “onlinear optics, the SP equation has also been derived as an integrable differential equation associated with pseudospherical surfaces [11]. The SP equation has been shown to be completely integrable [11, 12, 13, 14, 15]. The periodic and soliton solutions of the SP equation were found in [16, 17, 1”
- LETTER TO THE EDITOR: Solitary wave solutions of the short pulse equation (2006, background): “Recently, the Lax pair of the SPE, of the Wadati–Konno–Ichikawa (WKI) type, was rediscovered in [5], where also the second-order recursion operator of the SPE was presented and the chain of transformations v(x, t) = ( u2x + 1 ) −1/2 ; x = w(y, t), v(x, t) = wy(y, t); z(y, t) = arccoswy (2)”
- Well-posedness and small data scattering for the generalized Ostrovsky equation ✩ (2010, background): “On the other hand, the short-pulse equation (SPE) proved to be extremely interesting from a mathematical point of view due to the existence of an infinite hierarchy of conserved quantities [10], an ingenious transformation that related it to the integrable sine-Gordon equation and illustrated its co”