Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions (Memoirs of the American Mathematical Society) by Ioan Bejenaru (PDF)

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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 XC¹.

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