A transformation with symbolic computation and abundant new soliton-like solutions for the (1+2)-dimensional generalized Burgers equation

摘要

In this paper, an auto-Backlund transformation is presented for the generalized Burgers equation: u(t) + u(xy) + alphauu(y) + alphau(x)a(x)(-1) u(y) = 0 (alpha is constant) by using an ansatz and symbolic computation. Particularly, this equation is transformed into a (1 + 2)-dimensional generalized heat equation w(t) + w(xy) = 0 by the Cole-Hopf transformation. This shows that this equation is C-integrable. Abundant types of new soliton-like solutions are obtained by virtue of the obtained transformation. These solutions contain n-soliton-like solutions, shock wave solutions and singular soliton-like solutions, which may be of important significance in explaining some physical phenomena, The approach can also be extended to other types of nonlinear partial differential equations in mathematical physics. [References: 17]