For the Cauchy problem of multidimensional quasilinear hyperbolic systems of diagonal form without self-interaction, the global existence of classical solutions with small initial data was shown in [13]. In this paper, we will first prove that the global solution will scatter to free linear waves in some weighted $L^p$ sense, then based on it, we will study the rigidity aspect of scattering problem for quasilinear waves.

中文翻译：

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一些多维拟线性双曲系统全局解的渐近行为

对于无自相互作用的多维对角型拟线性双曲系统的柯西问题，文献[13]给出了小初始数据经典解的全局存在性。在本文中，我们将首先证明全局解将在某种加权 $L^p$ 意义上散射到自由线性波，然后在此基础上，我们将研究拟线性波散射问题的刚度方面。