Monotonicity Conjectures and Sharp Stability for Solitons of the Cubic-Quintic NLS on R3
Abstract
This paper deals with the cubic-quintic nonlinear Schr\"odinger equation on R3. Two monotonicity conjectures for solitons posed by Killip, Oh, Pocovnicu and Visan are completely resolved: one concerning frequency monotonicity, and the other concerning mass monotonicity. Uniqueness of the energy minimizer is proved. Then sharp stability of the solitons is established. And classification of normalized solutions is first presented.
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