Book Review: The defocusing NLS equation and its normal form

Orbital stability in the cubic defocusing NLS equation: I. Cnoidal periodic waves

Periodic waves of the one-dimensional cubic defocusing NLS equation are considered. Using tools from integrability theory, these waves have been shown in [4] to be linearly stable and the Floquet–Bloch spectrum of the linearized operator has been explicitly computed. We combine here the first four conserved quantities of the NLS equation to give a direct proof that cnoidal periodic waves are or...

The Semiclassical Limit of the Defocusing NLS Hierarchy

We establish the semiclassical limit of the one-dimensional defocusing cubic nonlinear Schrödinger (NLS) equation. Complete integrability is exploited to obtain a global characterization of the weak limits of the entire NLS hierarchy of conserved densities as the field evolves from reflectionless initial data under all the associated commuting flows. Consequently, this also establishes the zero...

20 07 Invariant Measures for the Defocusing Nls

We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane R 2. We also prove an estimate giving some intuition to what may happen in 3 dimensions. Résumé. On démontre l'existence et l'invariance d'une mesure de Gibbs par le flot de l'´ equation de Schrödinger non linéaire posée sur le disque du ...

Book review: The Periodic Table: Its Story and Its Significance

Critique of Novel/ Precedence of Form to Content: Review of the Book Thirst: Mehdi Ebrahimi Lame