We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed with respect to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially localized at one side of a lattice (skin effect), it is expected that the wave dynamics are governed by amplification or decay until reaching the boundaries, even in the presence of dissipation. Our analytical results, and experimental demonstrations in an active electrical-transmission-line metamaterial, reveal that nonlinearity is a crucial tuning parameter in mediating a delicate interplay between nonreciprocity, dispersion, and dissipation. Consequently, undistorted unidirectional solitonic pulses are supported both for low and high nonreciprocity and pulse amplitude. The proposed mechanism facilitates robust pulse propagation in signal-processing and energy-transmission applications.

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• Control theory
• Non-reciprocal propagation
• Skin effect
• Wave scattering
• Metamaterials
• Non-Hermitian systems
• Smart materials
• Solitons