  Results are reported from an amplitude analysis of the $B^+\to D^+D^-K^+$
decay. The analysis is carried out using LHCb proton-proton collision data
taken at $\sqrt{s}=7,8,$ and $13$ TeV, corresponding to a total integrated
luminosity of 9 fb$^{-1}$. In order to obtain a good description of the data,
it is found to be necessary to include new spin-0 and spin-1 resonances in the
$D^-K^+$ channel with masses around 2.9 GeV$/c^2$, and a new spin-0 charmonium
resonance in proximity to the spin-2 $\chi_{c2}(3930)$ state. The masses and
widths of these resonances are determined, as are the relative contributions of
all components in the amplitude model, which additionally include the vector
charmonia $\psi(3770)$, $\psi(4040)$, $\psi(4160)$ and $\psi(4415)$ states and
a nonresonant component.
