Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.

中文翻译：

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扩展（2 + 1）维KdV方程的混合有理块孤波解

基于双线性方法，通过三线性形式的辅助函数的不同假设，构造了扩展的（2 + 1）维KdV方程的有理块和混合块孤波解。发现有理块在空间平面的所有方向上都代数衰减，并且其振幅具有一个最大值和两个最小值。一种混合溶液描述了一个团块和一个线孤波之间的相互作用，在不同的参数下表现出裂变和融合现象。另一种混合溶液表示一个团块与两个平行线孤立波相互作用，其中团块的演化产生二维流氓波。这表明这三个有趣的现象存在于相应的物理模型中。