English

Scattering theory of the nonlinear wave equations on lattices

Analysis of PDEs 2025-07-28 v1

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.

Keywords

Cite

@article{arxiv.2507.19160,
  title  = {Scattering theory of the nonlinear wave equations on lattices},
  author = {Jiajun Wang},
  journal= {arXiv preprint arXiv:2507.19160},
  year   = {2025}
}

Comments

31 pages, no figures