Near Soliton Evolution for Equivariant Schrödinger Maps in Two Spatial Dimensions

Near Soliton Evolution for Equivariant Schrödinger Maps in Two Spatial Dimensions Synopsis

The authors consider the Schrödinger Map equation in 2 1 dimensions, with values into S². This admits a lowest energy steady state Q , namely the stereographic projection, which extends to a two dimensional family of steady states by scaling and rotation. The authors prove that Q is unstable in the energy space ?¹. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology XC?¹.