Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions
Author | : Ioan Bejenaru |
Publisher | : American Mathematical Soc. |
Total Pages | : 120 |
Release | : 2014-03-05 |
ISBN-10 | : 9780821892152 |
ISBN-13 | : 0821892150 |
Rating | : 4/5 (52 Downloads) |
Download or read book Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions written by Ioan Bejenaru and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.