Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 39, Issue -, Pages 21-28Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2016.02.031
Keywords
Integrable systems; Solitons; Short pulse equation; Single-cycle pulse
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Funding
- Max Planck Institute for Mathematics
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By means of transformations to nonlinear Klein-Gordon equations, we show that a generalized short pulse equation is integrable in two (and, most probably, only two) distinct cases of its coefficients. The first case is the original short pulse equation (SPE). The second case, which we call the single-cycle pulse equation (SCPE), is a previously overlooked scalar reduction of a known integrable system of coupled SPEs. We get the Lax pair and bi-Hamiltonian structure for the SCPE and show that the smooth envelope soliton of the SCPE can be as short as only one cycle of its carrier frequency. (C) 2016 Elsevier B.V. All rights reserved.
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