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

In this paper, an auto-Backlund transformation is presented for the generalized Burgers equation: ut + uxy + αuuy + αux∂−1xuy = 0 (α is constant) by using an ansatz and symbolic computation. Particularly, this equation is transformed into a (1 + 2)-dimensional generalized heat equation ωt + ωxy = 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.

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