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Multiple Soliton Solutions of Alice–Bob Boussinesq Equations |
| Hui Li1, S. Y. Lou1,2** |
1School of Physical Science and Technology, Ningbo University, Ningbo 315211
2Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062
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| Cite this article: |
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Hui Li, S. Y. Lou 2019 Chin. Phys. Lett. 36 050501 |
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Abstract Three Alice–Bob Boussinesq (ABB) nonlocal systems with shifted parity ($\hat{P}_{\rm s}$), delayed time reversal ($\hat{T}_{\rm d}$) and $\hat{P}_{\rm s}\hat{T}_{\rm d}$ nonlocalities are investigated. The multi-soliton solutions of these models are systematically found from the $\hat{P}_{\rm s}$, $\hat{T}_{\rm d}$ and $\hat{P}_{\rm s}\hat{T}_{\rm d}$ symmetry reductions of a coupled local Boussinesq system. The result shows that for ABB equations with $\hat{P}_{\rm s}$ and/or $\hat{T}_{\rm d}$ nonlocality, an odd number of solitons is prohibited. The solitons of the $\hat{P}_{\rm s}$ nonlocal ABB and $\hat{T}_{\rm d}$ nonlocal ABB equations must be paired, while any number of solitons is allowed for the $\hat{P}_{\rm s}\hat{T}_{\rm d}$ nonlocal ABB system. $t$-breathers, $x$-breathers and rogue waves exist for all three types of nonlocal ABB system. In particular, different from classical local cases, the first-order rogue wave can have not only four leaves but also five and six leaves.
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Received: 11 February 2019
Published: 17 April 2019
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| PACS: |
05.45.Yv
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(Solitons)
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11.30.Er
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(Charge conjugation, parity, time reversal, and other discrete symmetries)
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42.65.Tg
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(Optical solitons; nonlinear guided waves)
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| Fund: Supported by the National Natural Science Foundation of China under Grant No 11435005, and the K. C. Wong Magna Fund in Ningbo University. |
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