Lie symmetry analysis and conservation laws for multi-component burgers equations in higher dimensions

In this work, we extend the classical Burgers equation to a generalized [Formula: see text]-dimensional multi-component nonlinear system, capturing the interactions between multiple fields across higher dimensions, with applications in fluid dynamics, traffic flow, and nonlinear wave propagation in complex media. We derive the general formula for the Lie symmetry group of the system. By using the obtained symmetries, we reduce the original system to ordinary differential equations (ODEs). For these ODEs, we apply auxiliary equation methods and provide analytical formulas for exact solutions. As illustrative examples, we demonstrate the (3+1)-dimensional three-component Burgers equations and present various solution types. We also provide graphical representations of the solutions for selected parameter values. Finally, using the obtained symmetry, we derive conservation laws of the system. The conservation vectors corresponding to each symmetry generator are essential for understanding the system’s dynamical properties and energy conservation. These conservation vectors offer a valuable tool for further investigating the physical phenomena described by the multi-dimensional Burgers equations.