Nonlinear self-adjointness and conservation laws of the (3+1)-dimensional Burgers equation

Conservation laws are one of the most important gateways to understanding physical properties of various systems. They are important for investigating integrability and for establishing existence and uniqueness of solutions. They have been used for the development of appropriate numerical methods and construction of exact solutions of partial differential equations. They play an essential role in the development of numerical methods and provide an essential starting point for finding non-locally related systems and potential variables. In the present paper we consider the (3+1)-dimensional Burgers equation whose special solitonic localized structure was investigated in Dai and Yu (2014). We show that it is nonlinearly self-adjoint and use this fact to construct infinite but independent, non-trivial and simplified conserved vectors in general form.