Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions

Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions PDF Author: Ioan Bejenaru
Publisher: American Mathematical Soc.
ISBN: 0821892150
Category : Mathematics
Languages : en
Pages : 120

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Book Description
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.