Conditional similarity reductions of the (2 + 1)-dimensional KdV equation via the extended Lie group approach

The classical and nonclassical Lie group approaches are extended and applied to construct new conditional similarity reductions for nonlinear systems. The application of the method to a simple (2 + 1)-dimensional KdV equation results in not only the known conditional similarity reductions obtained by the modified Clarkson and Kruskal's direct method but also a great diversity of classical and nonclassical conditional similarity reductions.