Communications in Theoretical Physics >
Fifth-Order Alice-Bob Systems and Their Abundant Periodic and Solitary Wave Solutions*
Received date: 2019-06-08
Request revised date: 2019-07-28
Online published: 2019-10-11
Supported by
Sponsored by the National Natural Science Foundations of China under Grant(No. 11435005)
K. C. Wong Magna Fund in Ningbo University
Copyright
The study on the nonlocal systems is one of the hot topics in nonlinear science. In this paper, the well-known fifth-order integrable systems including the Sawada-Kotera (SK) equation, the Kaup-Kupershmidt (KK) equation and the fifth-order Koterweg-de Vrise (FOKdV) equation are extended to a generalized two-place nonlocal form, the generalised fifth-order Alice-Bob system. The Lax integrability of two sets of Alice-Bob systems for all the SK, KK and FOKdV type systems are explicitly given via matrix Lax pairs. The $\hat{P}\hat{T}$ symmetry breaking and symmetry invariant periodic and solitary waves for one set of nonlocal SK, KK and FOKdV system are investigated via a special travelling wave solution ansatz.
Zhao Qi-Liang , Jia Man , Lou Sen-Yue . Fifth-Order Alice-Bob Systems and Their Abundant Periodic and Solitary Wave Solutions*[J]. Communications in Theoretical Physics, 2019 , 71(10) : 1149 -1154 . DOI: 10.1088/0253-6102/71/10/1149
[1] |
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[2] |
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[3] |
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[4] |
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[5] |
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[6] |
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[7] |
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[8] |
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[9] |
|
[10] |
|
[11] |
|
[12] |
|
[13] |
|
[14] |
|
[15] |
|
[16] |
|
[17] |
T. Kakutani and H.Ono, J. Phys. Soc. Jpn. 26(1969) 1305.
|
[18] |
|
[19] |
|
[20] |
|
[21] |
|
[22] |
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[23] |
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[24] |
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[25] |
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[26] |
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[27] |
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