  Based on analyses of the mass and the strong decay features, $D_{s0}(2590)^+$
observed by LHCb collaboration is identified as a radial excitation of the
pseudoscalar $D_s$, and $D_{sJ}(3040)^+$ observed by BaBar collaboration is
identified as a radial excitation of $D_{s1}(2536)^\pm$. $D_{s0}(2590)^+$ is
possibly a pure $D_{s}(2~^1S_0)$ meson, both basic $D_{s1}(2536)^\pm$ and
radially excited $D_{sJ}(3040)^+$ are possibly the mixtures $D_s(nP_1)$ between
spin triplet $D_s(n~^3P_1)$ and spin singlet $D_s(n~^1P_1)$. In this
arrangement, their masses meet the linear behavior of the radial Regge
trajectory very well. In the $^3P_0$ strong decay model, the decay channels of
$D_{s0}(2590)^+$ are $D^{*0}K^+$ and $D^{*+}K^0$, the total decay width is
predicted with $\Gamma=76.12$ MeV. The main decay channels of $D_{sJ}(3040)^+$
are $D^{*0}K^+$/$D^{*+}K^0$ and $D^{*0}K^{*+}$/$D^{*+}K^{*0}$, the total decay
width is predicted with $\Gamma=283.46$ MeV. These numerical strong decay
results are consistent with the experiment data and support our arrangement.
The dimensionless strength creation parameter $\gamma$ plays an important role
in the calculation, and $\gamma=9.57$ is fixed through a comparison of the
predicted strong decay widths of $D^*_{s2}(2573)$ and $D^*_{s3}(2860)^{\pm}$
with experimental data.
