@article{Deng2026, 
author = {Shijie Deng and Bo Tang and Wenjing Yang and Kaili Liu and Huawei Wu},
title = {Three-wave, rogue wave and interaction solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito-Shallow-Water-Wave-like equation},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {2},
pages = {669-692},
keywords = {bilinear neural network method, Hirota bilinear transformation, Bell polynomial, (2+1)-dimensional nonlinear evolution equation, exact solutions},
url = {https://www.sciopen.com/article/10.3934/nhm.2026029},
doi = {10.3934/nhm.2026029},
abstract = {In this article, we focused on the bilinear neural network method to obtain the exact solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito-Shallow-Water-Wave-like equation. This method can also be applied to solve other nonlinear partial differential equations (NPDEs). Relying on Hirota bilinear transformation and Bell polynomial theories, we successfully constructed one-hidden-layer and multiple-hidden-layers models with assigned activation functions. Thereby, we derived many exact solutions for this equation including three-wave, rogue wave, and interaction solutions. To intuitively reflect features of these solutions, we depicted their three-dimensional, density, and curve graphs.}
}