We revisit the scattering problems for the 2D mass super-critical Schr\"{o}dinger and Klein-Gordon equations with radial data below the ground state in the energy space. We give an alternative proof of energy scattering for both defocusing and focusing cases using the ideas of Dodson-Murphy \citep{dodson2017new-radial}. Our results also include the exponential type nonlinearities which seems to be new for the focusing exponential NLS.

中文翻译：

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重新审视二维非线性薛定谔方程和 Klein-Gordon 方程的基态以下散射

我们使用能量空间中基态以下的径向数据重新审视二维质量超临界 Schr\"{o}dinger 和 Klein-Gordon 方程的散射问题。我们给出了散焦和聚焦情况下能量散射的替代证明使用 Dodson-Murphy \citep{dodson2017new-radial} 的思想。我们的结果还包括指数型非线性，这对于聚焦指数 NLS 来说似乎是新的。