Fifth-Order Alice-Bob Systems and Their Abundant Periodic and Solitary Wave Solutions*

Authors:
  • QIQi-Liang启亮Zhao赵
    Qi-Liang启亮Zhao赵
  • MAMan曼Jia贾
    Man曼Jia贾
  • SESen-Yue森岳Lou楼
    Sen-Yue森岳Lou楼
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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 P ^ 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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