Muhammad Qasim, Yao Fengping, Muhammad Zafarullah Baber
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引用次数: 0
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.
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.