Abstract
We consider a general class of variable coefficient Calogero–Degasperis equations. The complete Lie group classification is performed with the aid of the appropriate equivalence group. Lie symmetries are used to derive a number of reductions by constructing the corresponding optimal lists of one-dimensional subalgebras of the Lie symmetry algebras. Furthermore, a number of non-Lie reductions are given. One of the reduced equations is the variable coefficient potential KdV equation which is studied from the point of view of Lie group analysis.
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