In this work, the $(2+1)$-dimensional Kadomtsev–Petviashvili model is investigated. A novel variational scheme, namely, the variational transform wave method (VTWM), is successfully established to seek the solitary wave solution of the Kadomtsev–Petviashvili model. Furthermore, the fractal solitary solution of fractal Kadomtsev–Petviashvili model is also studied based on the local fractional derivative. Numerical examples are given to fully demonstrate that the VTWM is straightforward, efficient and attractive. Finally, the physical properties of solitary wave solutions are demonstrated by some 3D graphs.

中文翻译：

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(2+1)维KADOMTSEV-PETVIASHVILI模型及其分形模型的变分视角

在这项工作中，$（2+1）$研究了维 Kadomtsev-Petviashvili 模型。成功建立了一种新的变分方案，即变分变换波法（VTWM），以寻求 Kadomtsev-Petviashvili 模型的孤立波解。此外，还基于局部分数阶导数研究了分形Kadomtsev-Petviashvili模型的分形孤立解。给出的数值例子充分证明了VTWM的简单、高效和有吸引力。最后，通过一些 3D 图演示了孤立波解的物理性质。