The purpose of this note is to prove the existence of a conformal scattering operator for the cubic defocusing wave equation on a non-stationary background. The proof essentially relies on solving the characteristic initial value problem by the method developed by Hörmander. This method consists in slowing down the propagation speed of the waves to transform a characteristic initial value problem into a standard Cauchy problem.

中文翻译：

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用于非线性波动方程的特征柯西问题和共形散射的 Hörmander 方法

本笔记的目的是证明非平稳背景上三次散焦波动方程的共形散射算子的存在。证明本质上依赖于用Hörmander 开发的方法求解特征初值问题。该方法包括减慢波的传播速度，将特征初始值问题转化为标准柯西问题。