标题： rogue waves and instability arising from long-wave-short-wave resonance beyond the integrable regime 显示英文标题

标题： Rogue waves and instability arising from long-wave-short-wave resonance beyond the integrable regime

摘要： 我们从非可积区域中的长波-短波（LWSW）共振出发，数值地考虑不稳定性及局部模式。 我们研究椭圆函数周期波相对于次谐波扰动的稳定性和不稳定性，这些扰动的周期是椭圆波周期的倍数。 因此，我们发现了相应的dnoidal波的调制不稳定性（MI）。 在改变dnoidal波的参数时，可以通过哈密顿霍普夫分岔将光谱不稳定的dnoidal波转化为稳定状态。 对于snoidal波，我们发现MI与具有类似气泡谱的不稳定性之间的主要不稳定性场景的转变。 对于cnoidal波，我们产生了三种MI的变体。 不稳定状态的演化也被考虑，导致在椭圆波和连续波背景上形成异常波。 显示英文摘要

摘要： We consider instability and localized patterns arising from long wave-short wave (LWSW) resonance in the non-integrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, whose period is a multiple of the period of the elliptic waves. We thus find the modulational instability (MI) of the corresponding dnoidal waves. Upon varying parameters of dnoidal waves, spectrally unstable ones can be transformed into stable states via the Hamiltonian Hopf bifurcation. For snoidal waves, we find a transition of the dominant instability scenario between the MI and instability with a bubble-like spectrum. For cnoidal waves, we produce three variants of the MI. Evolution of the unstable states is also considered, leading to formation of rogue waves on top of the elliptic-wave and continuous-wave backgrounds.