Solving the (3+1)D Zakharov-Kuznetsov-Burgers equation using physics-informed neural networks

Abstract

The (3 + 1)-dimensional Zakharov-Kuznetsov-Burgers (ZKB) equation plays a pivotal role in modeling nonlinear wave propagation and dissipation phenomena in plasma dynamics. In this study, we develop a Physics-Informed Neural Network (PINN) framework tailored to accurately solve the ZKB equation with appropriate initial and boundary conditions. The proposed method successfully reconstructs lump and multi-soliton wave structures, exhibiting excellent agreement with analytical benchmarks. High-resolution 2D, 3D surface, and contour plots illustrate the dynamic evolution of nonlinear waves, while error heatmaps and training loss curves validate the model’s accuracy and stability. The PINN framework is implemented on [specify hardware, e.g., Intel i9 CPU, NVIDIA RTX GPU, 64 GB RAM], achieving efficient training times for high-dimensional computations. Moreover, potential applications in spatiotemporal structured light and coupled nonlinear systems are discussed, highlighting the broader significance of this approach in modern plasma physics and optics. This work emphasizes the robustness, efficiency, and versatility of PINNs in handling high-dimensional nonlinear partial differential equations, offering a promising computational alternative for future research in plasma physics, soliton theory, and applied mathematics.