2024年6月1日 · Benney–Luke equation, the estimation of water wave propagation on the water’s surface, is significantly important in studying the tension of water waves in physics. This paper focuses on the Bilinear Neural Network method (BNNM) to …

2020年11月9日 · This paper extends a method, called bilinear neural network method (BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this...

2024年1月1日 · Futhermore Liu [28] investigates some new exact analytical solutions of the (2+1)-dimensional fractional generalized Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–Konopelchenko equation via BNNM. Compared with Zhang’s BNNM model, Liu generalizes the activation function to the multivariate form.

2022年8月7日 · The interference wave solution of the gBS-like equation is obtained by using the bilinear neural network method (BNNM) and physical informed neural networks (PINNs). Interference waves are shown well via three-dimensional plots and density plots. Compared with PINNs, the bilinear neural network method is not only more accurate but also faster.

2024年10月1日 · This paper aims to discover new types of exact solutions for the (4 + 1)-dimensional BLMP-like equation utilizing the BNNM. The innovative aspect of this study lies in the comprehensive analysis of the multiple structures of the (4 + 1)-dimensional BLMP-like equation, which represents a novel and straightforward approach.

本文采用双线性神经网络方法（BNNM），利用神经网络统一各种经典的测试函数方法，获得了（3 + 1) 维 Hirota 双线性 (HB) 方程。 基于HB方程的Hirota形式，通过引入级数，构造了四种新的解，即呼吸器解、流氓波解、呼吸器块状孤子解以及周期波与二扭结波之间的相互作用解。 单层和多层神经元中的测试函数，例如 [4-2-2]和 [4-2-3]神经网络模型。 此外，我们还将它们与已经发布的内容进行了比较。 很明显，我们的结果与这些出版物中的结果不一致。 它们相应的动态特 …

2023年9月25日 · In this paper, the $$(3+1)$$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq (BKP-Boussinesq) equation was fully studied with the help of bilinear neural network method (BNNM) and symbolic computation, which can describe the interaction process of exponential local structures and …

In this paper, we introduce a novel Maple algorithm tailored for bilinear neural network methods (BNNM). This algorithm progresses from the initial NPDE to the final solutions, illustrating a new method for automatically constructing analytical solutions to NPDEs.

本文主要采用双线性神经网络的方法(bnnm)来构造非线性偏微分方程的精确解析解。 首先，本文对双线性神经网络的方法和非线性偏微分方程的背景与本文所需要的前置步骤进行了介绍。

本文借助双线性神经网络方法（BNNM）和符号计算，对\((3+1)\)维B型Kadomtsev–Petviashvili–Boussinesq (BKP-Boussinesq)方程进行了充分研究，可描述指数局部结构与浅水中长波传播的相互作用过程。