By a known transformation, (2+1)-dimensional Brioer–Kaup
equations are turned to a single equation. The classical Lie
symmetry analysis and similarity reductions are performed for this
single equation. From some of reduction equations, new exact
solutions are obtained, which contain previous results, and more
exact solutions can be created directly by abundant known
solutions of the Burgers equations and the heat equations.
The Exp-function method plays an important role in searching for analytic solutions of many nonlinear differential equations. In this paper, we prove that the balancing procedure in the method is unnecessary when the balanced nonlinear term is a product of the dependent variable under consideration and its derivatives. And in this case, the ansatz of the method can be simplified to be with less parameters so as to be easy to calculate.
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