Interaction induced deformation of two coupled XY spin chains

We study two coupled XY spin chains in the continuum limit with ferromagnetic interaction both along and between the chains. We find 2 pi twist soliton solutions for the difference in orientation angle of the spins along the chains. If we allow the chains to be elastic, they will deform (move apart) in the region of the soliton in order to reduce magnetic energy. The extent of deformation is a result of a balance between the gain in magnetic energy and elastic energy cost. We also generalize these results to the case of a soliton lattice.