Abstract

The direct method of Clarkson and Kruskal is used to study the symmetry reductions of the Burgers equation with linear damping. The classical similarity reductions reported previously is recovered. The new, nonclassical similarity reduction is obtained. The new similarity solution is given, and it is also obtained by means of the singular manifold method. The nonclassical method is used to demonstrate that the new exact solution is indeed a nonclassical similarity solution.

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