Non-Hermitian physics has drawn tremendous attention in both fundamental physics and potential applications. Recent progress has witnessed a surge of research on non-Hermitian skin effects (NHSEs), where wave dynamics exhibits unconventional behaviors like non-Hermitian amplifications/attenuations, sticky effects, and edge bursts. In previous studies, the dynamics of NHSEs was often treated as the propagation of a single wavepacket. Here, we provide a novel perspective by exploring the multiwavepacket dynamics of NHSEs. This is realized by introducing nonreciprocal long-range couplings into the non-Hermitian Hatano-Nelson (HN) model. It is shown that by tuning the coupling strengths based on the periodic boundary condition (PBC) spectrum, the emergence, number, propagation directions, and intensities of multiple wavepackets in the bulk can be effectively controlled. Based on the open boundary condition (OBC) spectrum, the full temporal evolution and physical origins of the non-Hermitian wavepackets can be exactly captured. The PBC and OBC spectra complement each other, enabling both flexible manipulation and rigorous interpretation of multiple wavepackets, forming a complete theoretical framework for NHSE multiwavepacket dynamics. Furthermore, beyond using the stationary spectrum to understand and control multiwavepacket dynamics, we elucidate the time-dependent excitation methods for manipulating the relative intensity of different wavepackets in systems with and without loss. In particular, we identify the crucial role of the real part of the excitation frequency in selectively exciting different wavepackets. Our results reveal the rich dynamic properties of NHSEs and offer new insights for non-Hermitian wave manipulations in both spatial and temporal domains.

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• Skin effect
• Non-Hermitian systems
• Numerical techniques
• Tight-binding model