Multiple Soliton Solutions of Alice–Bob Boussinesq Equations

Hui Li; S. Y. Lou

doi:10.1088/0256-307X/36/5/050501

Multiple Soliton Solutions of Alice–Bob Boussinesq Equations

Hui Li¹,
S. Y. Lou^1,2**

¹School of Physical Science and Technology, Ningbo University, Ningbo 315211
²Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062

Funds: 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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Received Date: February 10, 2019

Published Date: April 30, 2019

Abstract

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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[1]	Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 doi: 10.1103/PhysRevLett.80.5243 CrossRef Google Scholar
[2]	Konotop V V, Yang J K and Zezyulin D A 2016 Rev. Mod. Phys. 88 035002 doi: 10.1103/RevModPhys.88.035002 CrossRef Google Scholar
[3]	Ablowitz M J and Musslimani Z H 2013 Phys. Rev. Lett. 110 064105 doi: 10.1103/PhysRevLett.110.064105 CrossRef Google Scholar
[4]	Lou S Y 2018 J. Math. Phys. 59 083507 doi: 10.1063/1.5051989 CrossRef Google Scholar
[5]	Lou S Y and Huang F 2017 Sci. Rep. 7 869 doi: 10.1038/s41598-017-00844-y CrossRef Google Scholar
[6]	Lou S Y 2017 Chin. Phys. Lett. 34 060201 doi: 10.1088/0256-307X/34/6/060201 CrossRef Google Scholar
[7]	Jia M and Lou S Y 2018 Phys. Lett. A 382 1157 doi: 10.1016/j.physleta.2018.02.036 CrossRef Google Scholar
[8]	Lou S Y 2019 Stud. Appl. Math. 142 accepted doi: 10.1111/sapm.12265 CrossRef Google Scholar
[9]	Lou S Y 2019 arXiv:1901.02828 Google Scholar
[10]	Song Q C, Xiao D M and Zhu Z N 2017 Commun. Nonlinear Sci. & Numer. Simul. 47 1 doi: 10.1016/j.cnsns.2016.11.005 CrossRef Google Scholar
[11]	Modak S, Singh A and Panigrahi P 2016 Eur. Phys. J. B 89 149 doi: 10.1140/epjb/e2016-70130-7 CrossRef Google Scholar
[12]	Ablowitz M J and Musslimani Z H 2016 Nonlinearity 29 915 doi: 10.1088/0951-7715/29/3/915 CrossRef Google Scholar
[13]	Ji J L and Zhu Z N 2017 J. Math. Anal. Appl. 453 973 doi: 10.1016/j.jmaa.2017.04.042 CrossRef Google Scholar
[14]	Ablowitz M J and Musslimani Z H 2014 Phys. Rev. E 90 032912 doi: 10.1103/PhysRevE.90.032912 CrossRef Google Scholar
[15]	Dimakos M and Fokas A S 2013 J. Math. Phys. 54 081504 doi: 10.1063/1.4817345 CrossRef Google Scholar
[16]	Fokas A S 2016 Nonlinearity 29 319 doi: 10.1088/0951-7715/29/2/319 CrossRef Google Scholar
[17]	Rao J G, Cheng Y and He J S 2017 Stud. Appl. Math. 139 568 doi: 10.1111/sapm.12178 CrossRef Google Scholar
[18]	Rao J G, Zhang Y S, Fokas A S and He J S 2018 Nonlinearity 31 4090 doi: 10.1088/1361-6544/aac761 CrossRef Google Scholar
[19]	Yang B and Chen Y 2018 Nonl. Dyn. 94 489 doi: 10.1007/s11071-018-4373-0 CrossRef Google Scholar
[20]	Peng L, Yang X D and Lou S Y 2012 Commun. Theor. Phys. 58 1 doi: 10.1088/0253-6102/58/1/01 CrossRef Google Scholar
[21]	Hirota R 1971 Phys. Rev. Lett. 27 1192 doi: 10.1103/PhysRevLett.27.1192 CrossRef Google Scholar

[1]	WANG Jun-Min. Periodic Wave Solutions to a (3+1)-Dimensional Soliton Equation [J]. Chin. Phys. Lett., 2012, 29(2): 020203. doi: 10.1088/0256-307X/29/2/020203
[2]	CHEN Shou-Ting, ZHU Xiao-Ming, LI Qi, CHEN Deng-Yuan. N-Soliton Solutions for the Four-Potential Isopectral Ablowitz–Ladik Equation [J]. Chin. Phys. Lett., 2011, 28(6): 060202. doi: 10.1088/0256-307X/28/6/060202
[3]	LIU Yu. New Type Soliton Solutions to Korteweg-de Vries and Benjamin-Bona-Mahony Equations [J]. Chin. Phys. Lett., 2010, 27(9): 090201. doi: 10.1088/0256-307X/27/9/090201
[4]	YOU Fu-Cai, ZHANG Jiao, HAO Hong-Hai. Multi-Soliton Solutions of the Levi Equations [J]. Chin. Phys. Lett., 2009, 26(9): 090201. doi: 10.1088/0256-307X/26/9/090201
[5]	MO Jia-Qi. A Variational Iteration Solving Method for a Class of Generalized Boussinesq Equations [J]. Chin. Phys. Lett., 2009, 26(6): 060202. doi: 10.1088/0256-307X/26/6/060202
[6]	WU Yong-Qi. Periodic Wave Solution to the (3+1)-Dimensional Boussinesq Equation [J]. Chin. Phys. Lett., 2008, 25(8): 2739-2742.
[7]	LIN Ji, LOU Sen-Yue, WANG Ke-Lin. Multi-soliton Solutions of the Konopelchenko-Dubrovsky Equation [J]. Chin. Phys. Lett., 2001, 18(9): 1173-1175.
[8]	ZHANG Jie-fang. Multiple Soliton Solutions of the Dispersive Long-Wave Equations [J]. Chin. Phys. Lett., 1999, 16(1): 4-5.
[9]	WU Ying, YANG Xiaoxue. Soliton Chain Solutions to the Two-Dimensional Higher Order Korteweg de Vries Equations of Lax Hierarchy [J]. Chin. Phys. Lett., 1992, 9(2): 61-64.
[10]	YAN Zhida. MULTI-SOLITON SOLUTIONS OF COUPLED NONLINEAR SCHRODINGER EQUATIONS [J]. Chin. Phys. Lett., 1987, 4(4): 185-188.

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