Check the manual, find out what polarity. Usually it's center pin is POS. Also find out what the max voltage/amp/current is. It says 15v, but is that nominal voltage or max? If it's max, you're going to have a hard time finding a panel with a Voc of 15v or lower without DIYing something.
EDIT: timselectric makes a good point, that looks like more charging from a wall adapter, so it doesn't actually have an onboard solar charge controller. In that case, don't hook up solar directly, you'll need a separate solar charge controller.
Even worse, it might just be a dumb input, and expect the exterior power source to also monitor and do CC/CV (constant current/constant voltage) charging on the lithium battery inside, rather than just feeding it power and doing the CC/CV internally.