Abstract
In this paper, we consider a novel generalized Conde-Gordoa-Pickering equation with time-dependent coefficients by virtue of the Lie symmetry method. An equivalence group is constructed for the considered generalized nonlinear equation. A complete Lie group classification is performed with the aid of the equivalence group. A number of similarity reductions which reduce the generalized equation into ordinary differential equations are given, and several exact solutions are generated. Moreover, we discuss the integrable nature of the novel generalized equation, and particularly, determine cases of restricted coefficients under which the novel equation is Painlevé integrable.
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