Painlev, Test, Generalized Symmetries, Backlund Transformations and Exact Solutions to the Third-Order Burgers' Equations

摘要

In this paper, the Painlev, analysis is performed on the physical form of the third-order Burgers' equation, the Painlev, property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other equation are given by the symmetry transformation method. The Backlund Transformations of the equations are constructed based on the symmetries, respectively. Furthermore, the exact explicit solutions to the equations are investigated in terms of the symmetries, Backlund transformations and transformations of the equations.