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We present the basic concepts and our recent developments in the densityfunctional approaches with the Skyrme functionals for describing nucleardynamics at low energy. The time-dependent density-functional theory (TDDFT) isutilized for the exact linear response with an external perturbation. Fordescription of collective dynamics beyond the perturbative regime, we present atheory of a decoupled collective submanifold to describe for a slow motionbased on the TDDFT. Selected applications are shown to demonstrate the qualityof their performance and feasibility. Advantages and disadvantages in thenumerical aspects are also discussed.

progress of theoretical and experimental physics

Density functional approaches to collective phenomena in nuclei:  Time-dependent density-functional theory for perturbative and  non-perturbative nuclear dynamics