Instability of two interacting, quasi-monochromatic waves in shallow water

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schr\"odinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure

From prevention focus to adaptivity and creativity: the role of unfulfilled goals and work engagement

Whereas promotion focus is consistently linked to high adaptivity (i.e., adjustment to changes) and creativity (i.e., generation of useful and original ideas), prevention focus is commonly associated with low adaptivity and creativity. The present study uncovers the conditions under which prevention focus may also have positive effects on adaptivity and creativity. First, we hypothesize that trait-level promotion focus positively relates to day-level adaptivity as well as creativity. More importantly, we hypothesize that trait-level prevention focus positively relates to day-level adaptivity and creativity when day-level goal fulfilment is low (i.e., two-way interactions) and that these effects are stronger when day-level work engagement is high (i.e., three-way interactions). To test our hypotheses, we conducted a daily diary survey among 209 employees from different occupational sectors, over five working days. As expected, trait promotion focus was positively related to adaptivity and creativity. Furthermore, trait prevention focus positively related to both adaptivity and creativity when day-level goal fulfilment was low andday-level work engagement was high (3-way interactions). None of the two-way interaction effects of trait prevention focus and goal fulfilment was significant. Our findings suggest that prevention focus and unfulfilled goals jointly should not only be seen as threats, but also as opportunities for adaptation and creativity

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schr\"odinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schr\"odinger equations. Varying the relative strength of cross-phase and self-phase effects we show existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group velocity dispersion (GVD) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.Comment: Physical Review E, July, 199