Abstract
The functionally generalized variable separation solutions of a general KdV-type equations ut = uxxx + A(u,ux)uxx + B(u,ux) are investigated by developing the conditional Lie-Bäcklund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-Bäcklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.
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