The multiphase Whitham modulation equations with N phases have 2N characteristics which may be of hyperbolic or elliptic type. In this paper, a nonlinear theory is developed for coalescence, where two characteristics change from hyperbolic to elliptic via collision. Firstly, a linear theory develops the structure of colliding characteristics involving the topological sign of characteristics and multiple Jordan chains, and secondly, a nonlinear modulation theory is developed for transitions. The nonlinear theory shows that coalescing characteristics morph the Whitham equations into an asymptotically valid geometric form of the two-way Boussinesq equation, that is, coalescing characteristics generate dispersion, nonlinearity and complex wave fields. For illustration, the theory is applied to coalescing characteristics associated with the modulation of two-phase travelling wave solutions of coupled nonlinear Schrödinger equations, highlighting how collisions can be identified and the relevant dispersive dynamics constructed.

N相的多相Whitham调制方程具有2 N可能是双曲线或椭圆形的特征。在本文中，开发了一种用于合并的非线性理论，其中两个特征通过碰撞从双曲线变为椭圆。首先，线性理论开发了具有特征拓扑符号和多个约旦链的碰撞特征结构，其次，开发了用于跃迁的非线性调制理论。非线性理论表明，凝聚特征使Whitham方程变形为双向Boussinesq方程的渐近有效几何形式，也就是说，凝聚特征会产生色散，非线性和复杂波场。为了说明，