To find the group invariant solution, a new shifted parity and delayed time reversal symmetries are used in order to construct Alice–Bob systems. With the help of simple assumptions and of the [Formula: see text] symmetry, the intrinsic two-place model of the Sawada–Kotera (SK) system is elucidated. A new form of the [Formula: see text]-soliton solution for the nonlocal SK equation is obtained, and dynamic properties of the [Formula: see text]-soliton solutions with different values are discussed, respectively. In addition, the breather solution for the AB–SK system is also explicitly identified.

中文翻译：

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Alice-Bob 系统中非局部 Sawada-Kotera 方程的精确解

为了找到群不变解，使用新的移位奇偶校验和延迟时间反转对称性来构建 Alice-Bob 系统。在简单假设和 [公式：见正文] 对称性的帮助下，阐明了 Sawada-Kotera (SK) 系统的内在两位模型。得到了非局域SK方程的[公式：见正文]-孤子解的一种新形式，并分别讨论了[公式：见正文]-孤子解的不同取值的动力学性质。此外，还明确确定了 AB-SK 系统的呼吸器解决方案。