Boundary Giant Magnons and Giant Gravitons

We construct the full set of boundary giant magnons on $$\mathbb{R}$\times S^{2}$attachedtothemaximal$Z=0$ giant graviton by mapping from the general solution to static sine-Gordon theory on the interval and compute the values of $\mathrm{\Delta }-J$ at finite $J$, including the leading order corrections when $J$ is large. We then consider the Born-Infeld theory of the giant graviton itself to construct BIon spike solutions that correspond to the world volume description of the boundary giant magnons at finite $J$.