We construct a family of eigenfunction solutions of the Lax pair of the Kadomtsev–Petviashvili 1 (KP1) equation, which is expressed in terms of the Taylor coefficients of a fundamental exponential function associated with the Lax pair. Using the binary Darboux transformation, the higher-order rogue waves on a solitonic background of the KP1 equation are obtained by multiple soliton interactions. In fact, these solitons can evolve to significant and strongly localized transient waves during directional evolution, similarly to KP2 shallow-water interactions. We conjecture that the $n\text{th}$-order rogue wave solution evolves in the form of a triangular extreme wave pattern that consists of $\frac{n(n+1)}{2}$ solitonic lumps in the intermediate time, while only $n+1$ parallel line solitons possessing equal height are present before and after the initiation of collision dynamics. Such fascinating higher-order rogue waves have not yet been reported in the context of this $2+1$ dimensional integrable system. These exact solutions are particularly relevant for the fundamental understanding of extreme wave events in a variety of physical systems, such as plasma and solids.

我们构建了 Kadomtsev-Petviashvili 1 (KP1) 方程的 Lax 对的一系列特征函数解，它用与 Lax 对相关的基本指数函数的泰勒系数表示。使用二元 Darboux 变换，KP1 方程的孤子背景上的高阶流氓波是通过多个孤子相互作用获得的。事实上，这些孤子在定向演化过程中可以演化为显着且强局域化的瞬态波，类似于 KP2 浅水相互作用。我们推测，$n\text{日}$-阶流氓波解决方案以三角形极端波模式的形式演变，其中包括 $\frac{n(n+1)}{2}$ 中间时间的孤子团块，而只有 $n+1$在碰撞动力学开始之前和之后都存在具有相等高度的平行线孤子。在此背景下尚未报道过如此迷人的高阶流氓波$2+1$维可积系统。这些精确解与对各种物理系统（例如等离子体和固体）中的极端波事件的基本理解特别相关。