Nonlocal symmetry analysis, explicit solutions and conservation laws for the fourth-order Burgers' equation

The Painlevé analysis is carried out on the physical form of the fourth order Burgers' equation. Then, nonlocal symmetries of the equation are constructed. Also, linearizations are derived based on the symmetries. In particular, the explicit solution of the equations are presented in terms of Hopf-Cole transformations. Furthermore, nonlinear self-adjointness and conservation laws of potential equation are investigated with symmetries.