Abstract Non-reciprocal interactions, featured with an asymmetric relation between action and reaction, underpin exotic phenomena across living and artificial systems. Albeit extensively studied, they have been largely underexplored in nonlinear interactions of waves. In this work, we report an unusual impulse-momentum relationship for an optical solitary wave whose internal interactions are non-reciprocal. The solitary wave gains either an enhanced or a reversed momentum relative to an impulse that is applied to one of its two components. In the regime where the solitary wave is not broken down, the impulse-momentum relationship is found to be linear, yet its slope is unusual - either exceeding one or even being negative. Our results may initiate more fundamental considerations related to non-reciprocal wave interactions that are useful for designing novel non-Hermitian devices.
Zhuang et al. (Mon,) studied this question.