Nonlocal symmetry analysis and conservation laws to an third-order Burgers equation

They are of first order, second order, third order 27 and fourth order, respectively. The third-order Burg28 ers equation, similar to the second-order ones, appear 29 in many physical and engineering fields [8–10], such 30 as the plasma physics and fluid mechanics. In addi31 tion, these equations play a key role in nonlinear the32 ory and mathematical physics, in particular in the inte33 grable system, soliton theory, nonlinear wave theory, 34 and so on. It is to be noted that Eq. (3) is the dissipative 35 Burgers equation; by using the Hopf–Cole transforma36 tion, this equation can be reduced the heat equation 37 ut − uxx = 0. Moreover, the third equation in Eq. (4) 38 is the well-known Sharma–Tasso–Olver (STO) equa39 tion. The Burgers equation and the STO equation were 40 investigated in many papers such as [1–19]. In paper 41