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math.AP2025
Scattering theory of the nonlinear wave equations on lattices
Jiajun Wang
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…
math.AP2024
The well-posedness and scattering theory of nonlinear Schrödinger equations on lattice graphs
Jiajun Wang
In this paper, we introduce a novel first-order derivative for functions on a lattice graph, which extends the discrete Laplacian and generalizes the theory of discrete PDEs on lat…
math.AP2024
The well-posedness of generalized nonlinear wave equations on the lattice graph
Bobo Hua, Jiajun Wang
In this paper, we introduce a novel first-order derivative for functions on a lattice graph, and establish its weak (1, 1) estimate as well as strong (p, p) estimate for p > 1 in w…