Fifth-Order Alice-Bob Systems and Their Abundant Periodic and Solitary Wave Solutions* |
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Authors: | Qi-Liang Zhao Man Jia Sen-Yue Lou |
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Institution: | 1. School of Physical Science and Technology, Ningbo University, Ningbo 315211, China;2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China |
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Abstract: | 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. |
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Keywords: | Alice-Bob SK equarions Alice-Bob KK equations periodic and solitary waves |
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