Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions
Mar 2014 · American Mathematical Soc.
Ebook
108
Pages
About this ebook
The authors consider the Schrödinger Map equation in 2+1 dimensions, with values into \mathbb{S}^2. 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 \dot H^1. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology X \subset \dot H^1.
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 \dot H^1. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology X \subset \dot H^1.
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