The ‘japonica‘ of Japonica Plants is, of course, a specific epithet meaning ‘from Japan’. Botanical Latin is wonderful for many reasons but its ability to label a plant with an instant description or location is one of the best. Here are some more specific names connected with Asia.
nipponicum from Japan
yedoensis, yesoensis, yezoensis from Tokyo
yezoalpinus from the mountains of Hokkaido, Japan
chinensis, sinensis, sinica, cathayense from China
pekinensis from Beijing
setschwanensis, sichuanicus, szechuanicus from Sichuan province
emeiensis from Mt Emei, a botanical hotspot in Sichuan
guizhouensis, kouytchensis from Guizhou province
koreanus, coreanus from Korea
siamensis from Thailand
tibetanus, tibeticus from Tibet
taiwanensis, formosanus from Taiwan
Many of these names were checked at http://davesgarden.com/guides/botanary/ which is an excellent resource if you would like to find out more.