论文标题
多相调制理论中合并特征的非线性理论
Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory
论文作者
论文摘要
具有$ n $阶段的多相WHITHAM调制方程具有$ 2N $的特性，可能是双曲线或椭圆类型的。在本文中，有一个非线性理论是为了结合的，其中两个特征从双曲线变为椭圆形，通过碰撞变化。首先，线性理论发展了涉及特征和多个约旦链的拓扑特征的碰撞特征的结构，其次是为过渡而开发了非线性调制理论。非线性理论表明，合并特征将whitham方程变为双向boussinesq方程的渐近有效的几何形式。也就是说，合并特征会产生分散，非线性和复杂的波场。为了说明，该理论应用于与耦合非线性schrödinger方程的两相旅行波解的合并特征，突出了如何识别碰撞以及构建相关的分散动力学。
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.
