Near soliton evolution for equivariant Schrödinger maps in two spatial dimensions
Author(s)
Bibliographic Information
Near soliton evolution for equivariant Schrödinger maps in two spatial dimensions
（Memoirs of the American Mathematical Society, no. 1069）
American Mathematical Society, c2013
- Other Title
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Near soliton evolution for equivariant Schroedinger maps in two spatial dimensions
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Note
"March 2014, volume 228, number 1069 (first of 5 numbers)."
Includes bibliographical references (p. 107-108)
Description and Table of Contents
Description
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.
Table of Contents
- Introduction An outline of the paper The Coulomb gauge representation of the equation Spectral analysis for the operators H, H ~
- the X,LX spaces The linear H ~ Schrödinger equation The time dependent linear evolution Analysis of the gauge elements in X,LX The nonlinear equation for ? The bootstrap estimate for the ? parameter The bootstrap argument The ?¹ instability result Bibliography
by "Nielsen BookData"
