We present exact explicit Peregrine soliton solutions based on a periodic-wave background caused by the interference in the vector cubic-quintic nonlinear Schrödinger equation involving the self-steepening effect. It is shown that such periodic Peregrine soliton solutions can be expressed as a linear superposition of two fundamental Peregrine solitons of different continuous-wave backgrounds. Because of the self-steepening effect, some interesting Peregrine soliton dynamics such as ultrastrong amplitude enhancement and rogue wave coexistence are still present when they are built on a periodic background. We numerically confirm the stability of these analytical solutions against non-integrable perturbations, i.e., when the coefficient relation that enables the integrability of the vector model is slightly lifted. We also demonstrate the interaction of two Peregrine solitons on the same periodic background under some specific parameter conditions. We expect that these results may shed more light on our understanding of the realistic rogue wave behaviors occurring in either the fiber-optic telecommunication links or the crossing seas.

我们提出了基于周期波背景的精确显式Peregrine孤子解，该周期波背景是由涉及自增强效应的矢量三次五阶非线性Schrödinger方程中的干扰引起的。结果表明，这种周期性的Peregrine孤子解可以表示为连续波背景不同的两个基本Peregrine孤子的线性叠加。由于具有自增强作用，当将它们构建在周期性背景上时，仍然存在一些有趣的百富勤孤子动力学，例如超强振幅增强和流氓波共存。我们在数值上证实了这些分析解决方案对不可积分扰动的稳定性，即当使矢量模型可积分性的系数关系略微升高时。我们还演示了在某些特定参数条件下，两个Peregrine孤子在相同周期背景下的相互作用。我们希望这些结果可能有助于我们更好地理解在光纤电信链路或跨海中发生的实际流浪行为。