Scattering below the ground state for the 2D non-linear Schrödinger and Klein-Gordon equations revisited

We revisit the scattering problems for the 2D mass super-critical Schrödinger 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 the defocusing and focusing cases using the ideas in the work of Dodson and Murphy [Proc. Am. Math. Soc. 145, 4859 (2017)]. Our results also include the exponential type nonlinearities, which seem to be new for the focusing exponential non-linear Schrödinger equation.