This paper investigates wavepacket dynamics in non-Hermitian lattice systems and reveals a surprising phenomenon: The simultaneous propagation of two distinct wavefronts, one traveling at the non-Hermitian velocity and the other at the Hermitian velocity. We show that this dual-front behavior arises naturally in systems governed by a pseudo-Hermitian Hamiltonian. Using the paradigmatic Hatano-Nelson model as our primary example, we demonstrate that this coexistence is essential for understanding a wide array of unconventional dynamical effects, including abrupt “non-Hermitian reflections”, sudden shifts of Gaussian wavepackets, and disorder-induced emergent packets seeded by the small initial tails. We present analytic predictions that closely match numerical simulations. These results may offer new insight into the topology of non-Hermitian systems and point toward measurable experimental consequences.

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• Skin effect
• Disordered systems
• Lattices
• Non-Hermitian systems
• Su-Schrieffer-Heeger model