  In this paper, we study the novel nonlinear wave structures of a
(2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its
analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear
method, and in particular, the hybrid solution of lump, breather and line
soliton are derived by the long wave limit method. In addition to soliton
solutions, similarity reduction, including similarity solutions (also known as
group-invariant solutions) and non-autonomous third-order Painlev\'e equations,
is achieved through symmetry analysis. The analytic results, together with
illustrative wave interactions, show interesting physical features, that may
shed some light on the study of other variable-coefficient nonlinear systems.
