We consider finite-energy equivariant solutions for the wave map problem from to which are close to the soliton family. We prove asymptotic orbital stability for a codimension-two class of initial data which is small with respect to a stronger topology than the energy.
"A codimension-two stable manifold of near soliton equivariant wave maps." Anal. PDE 6 (4) 829 - 857, 2013. https://doi.org/10.2140/apde.2013.6.829