Abstract
This paper is an application of the similarity transformations method via Lie-group theory. This method is applied to the (3 + 1)-dimensional Burgers system to derive its invariant solutions. The Burgers system has many physical applications in fluid mechanics, heat conduction, plasma physics, traffic flows, and in some others like acoustic transmission and structure of shock waves. Since Burgers system consists of a system of nonlinear partial differential equations (PDEs), and therefore, it is a difficult task to obtain its exact solution. A system of PDEs is reduced into a system of ODEs and finally solved by making appropriate assumptions and choice of arbitrary functions and constants appeared therein. Hence, the obtained exact solutions compromised multisolitons, kink waves, periodic multisolitons, elastic mutisolitons and stationary waves.
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