Explicit wave solutions profile of (3+1)-dimensional Bateman–Burgers equation via bilinear neural network method

IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY The European Physical Journal Plus Pub Date : 2025-03-15 DOI:10.1140/epjp/s13360-025-06159-6
Muhammad Qasim, Yao Fengping, Muhammad Zafarullah Baber
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Abstract

This article explores the (3+1)-dimensional Bateman–Burgers equation using the bilinear neural network technique. Single and double layers of neural networks are built to construct different bilinear neural network models such as “4-3-1” and “4-2-2-1” by using specific activation functions. The interaction solution and periodic type-l solutions were extracted for this equation. The (3+1)-dimensional Bateman–Burgers equation has many applications in traffic flow, fluid mechanics, gas dynamics, and nonlinear acoustics. For enhancing the graphical representation of the dynamic behavior and the physical attributes of particular solutions, the computing tool Mathematica 13.1 was used for generating 3D visualizations, 2D graphical representations, and density mappings. The methodology used in this article improves the study of nonlinear partial differential equations that arise in different complex phenomena. In the end, we believe that these solutions will play a role in the understanding of some high-order equation nonlinear phenomena.

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本文利用双线性神经网络技术探讨了 (3+1) 维 Bateman-Burgers 方程。通过使用特定的激活函数,建立了单层和双层神经网络,构建了 "4-3-1 "和 "4-2-2-1 "等不同的双线性神经网络模型。提取了该方程的交互解和周期型-l 解。(3+1)-dimensional Bateman-Burgers 方程在交通流、流体力学、气体动力学和非线性声学中有着广泛的应用。为了增强对特定解的动态行为和物理属性的图形表示,我们使用了 Mathematica 13.1 计算工具来生成三维可视化、二维图形表示和密度映射。本文使用的方法改进了对不同复杂现象中出现的非线性偏微分方程的研究。最后,我们相信这些解决方案将在理解某些高阶方程非线性现象中发挥作用。
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来源期刊
The European Physical Journal Plus
The European Physical Journal Plus PHYSICS, MULTIDISCIPLINARY-
CiteScore
5.40
自引率
8.80%
发文量
1150
审稿时长
4-8 weeks
期刊介绍: The aims of this peer-reviewed online journal are to distribute and archive all relevant material required to document, assess, validate and reconstruct in detail the body of knowledge in the physical and related sciences. The scope of EPJ Plus encompasses a broad landscape of fields and disciplines in the physical and related sciences - such as covered by the topical EPJ journals and with the explicit addition of geophysics, astrophysics, general relativity and cosmology, mathematical and quantum physics, classical and fluid mechanics, accelerator and medical physics, as well as physics techniques applied to any other topics, including energy, environment and cultural heritage.
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