To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Bäcklund transformation and its bilinear formation, the symmetry breaking soliton, lump and breather solutions of this system are derived with the aid of some ansatze functions. Figures show these fascinating symmetry breaking structures of the explicit solutions.

中文翻译：

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Kadomtsev–Petviashvili方程的显式对称破坏解

为了描述两个相关事件，Lou通过移位奇偶校验，时间反转和电荷共轭的对称性构造了Alice–Bob（AB）系统。在本文中，建立了Kadomtsev–Petviashvili方程的耦合AB系统，该系统是自然科学中有用的模型。通过引入扩展的Bäcklund变换及其双线性形式，借助于一些解析函数，得出了该系统的对称打破孤子，集总和通气解。图显示了显式解的这些令人着迷的对称破坏结构。