标题： 孤波在非简并三波混频中的调制不稳定性：相位对称性的作用 显示英文标题

标题： Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

摘要： 我们展示如何将Zakharov和Rubenchik [Sov. Phys. JETP{\bf 38}, 494 (1974)] 对非线性薛定谔方程(NLS)中孤立波调制不稳定性(MI)的解析方法推广到具有两个相位对称性的模型。 作为此类模型的典型例子，研究了由于群速度色散(GVD)导致的三波参量空间孤子的MI。 我们发现了一种新的颈部不稳定性分支，该分支在正常GVD情况下主导了通常的蛇形MI。 因此，产生的非线性演化与仅具有单个相位对称性的案例在本质上有所不同。 显示英文摘要

摘要： We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.