Scattering theory of the nonlinear wave equations on lattices

Abstract: In this paper, I will summarize the uniform decay estimates of the discrete wave equations (DW) established by the oscillatory integral theory in [Sch98, BCH23, BCH24], and combine the abstract framework of the scattering theory of the dispersive equations established in [Str81] to finally establish the scattering theory of the discrete nonlinear wave equations (DNLW), including the existence of the wave operators and the asymptotic completeness. In addition, I will establish the scattering theory again by the Strichartz estimate.