This code should work:
p1 <- ggplot(iris, aes(Sepal.Length)) +
geom_density() +
ylim(limits = c(0, 1.25))+
facet_wrap(~ Species)
p2 <- ggplot(iris, aes(Sepal.Length)) +
geom_density() +
ggtitle("") + # ad empty title as place holder
labs(y = "", x = "") + # hide axis labels
ylim(limits = c(0, 1.25)) + # y axis values should be fixed in both plots
coord_fixed(ratio=20/1) + # ratio of x- and y-axis to reduce width of plot
theme(axis.ticks.y = element_blank(), axis.text.y = element_blank(), axis.line.y = element_blank(),
plot.margin=unit(c(0,0,0.65,-10), "lines")) # margin between plots = "0.65"
I fiddled a bit and used just different styling options to produce this result. If you have more plots than this one I would recommend to use one theme for all.
You can use either the multiplot function that you are already using
multiplot(p1, p2, cols = 2)
or you install the packages gridExtra and grid and use that one:
grid.arrange(p1, p2, ncol=2)
Hope this helps!