The theory of optimal control together with that of transient probe absorption spectroscopy are applied for control and detection of molecular wave packet dynamics in the weak response regime. We obtain a globally optimal pump–dump control field which drives the initial state to the predefined target, focused at the inner-turning point region of the electronic ground state potential. As for the...

We study the dynamics of corotational wave maps from $\mathbb R^{1+2} \rightarrow \mathbb S^2$ at threshold energy. It is known that topologically trivial with energy $< 8\pi$ are global and scatter to a constant map. In this work, we prove map equal $8\pi$ globally defined scatters in one time direction, other either scatters, or breaks down finite converges superposition two harmonic maps. Th...

Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave "clusters" consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a clu...