Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended G G ′       -expansion method, substituting the solutions obtained into the cor...

The Burgers’ equation first appeared in the paper by Bateman [3], who mentioned two of the essentially steady solutions. Due to extensive works of Burgers [4] involving the Burgers’ equation especially as a mathematical model for the turbulence, it is known as Burgers’ equation. The equation is used as a model in fields as wide as heat conduction [5], gas dynamics [13], shock waves [4], longitu...

We investigate solution properties of a class of evolutionary partial differential equations (PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. A recently developed two-step iterative method (Chiu et al., JCP, 228, (2009), pp. 8034-8052) i...

Non-local transformation, which connects the 3-dimensional Burgers-type equation with a linear heat equation, is constructed. Via this transformation, nonlinear superposition formulae for solutions are obtained and the conditional non-local symmetry of this equation is studied. The multidimensional generalization of the Burgers equation L1(u) = u0 − u|∇u| − u = 0, (1) is called further the Burg...

In this paper, a two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform d...

Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...

Considering the fractal structure of space-time, a Burgers – Korteweg – de Vries (BKdV) type equation is obtained. Particularly, if the motions of the “non-differentiable fluid” are irrotational, the BKdV type equation is reduced to a non-linear Schrödinger type equation. In this case, the scalar complex velocity field simultaneously becomes wave function.