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\textbf{SPEAKER}:
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%\textbf{SPEAKER}:
Joseph Lindgren, University of Kentucky
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{\bf TITLE}:
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Lyapunov stability of Ground States for focussing cubic NLS in 1-D
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{\bf ABSTRACT:}\\
We discuss orbital stability of ground state (equilibrium) solutions
for a 1-D cubic nonlinear focussing Schr\"odinger equation,
\[
iu_{t}+\Delta u-|u|^{2}u=0,
\]
 under perturbations of $H^{1}(R)$ initial data. Stability of equilibrium
solutions is an important condition for being able to use theoretical
models in physical applications. Following a paper due to Michael
I. Weinstein (1988), our method of proof is a generalization of Lyapunov
stability theory for finite dimensional systems. We rely on long-time
existence of a unique $H^{1}(R)$ solution (Ginibre-Velo, 1977).
The ground states, which are energy minimizing solutions, have soliton-like
profiles.
   


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