Scattering for the one-dimensional Klein–Gordon equation with exponential nonlinearity
Scattering for the one-dimensional Klein–Gordon equation with exponential nonlinearity
We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein-Gordon equation (NLKG) with exponential nonlinearity in the one spatial dimension with data in the energy space $H^1(\mathbb{R}) \times L^2(\mathbb{R})$. We prove that any energy solution has a global bound of the $L^6_{t,x}$ space-time norm, …