5 papers
Heisenberg Uniqueness Pairs for a Hyperbola Branch: Supercritical Nonuniqueness for Shifted Lattice Crosses
Zhiqiang Wan
We study Heisenberg uniqueness for the positive hyperbola branch and shifted lattice crosses in the supercritical regime . We resolve the infinite-dimensionality clause of…
The Cauchy problem for the improved Boussinesq equation with spatially quasi-periodic initial data
Zhiqiang Wan, Wenji Wu, Heng Zhang
We study the Cauchy problem for the improved Boussinesq equation \[ u_{tt}-u_{xx}-u_{xxtt}-(u^2)_{xx}=0 \] on the real line with spatially quasi-periodic initial data. For a non-re…
Dispersive estimates for discrete Klein-Gordon equations on one-dimensional lattice with quasi-periodic potentials
Zhiqiang Wan, Heng Zhang
We prove dispersive estimates for the discrete Klein--Gordon equation on with small real-analytic quasi-periodic potentials, showing that…
Observable sets for Schrödinger equations on combinatorial graphs
Zhiqiang Wan, Heng Zhang
We study observable sets for Schrödinger equations on combinatorial graphs. For one-dimensional lattice Schrödinger operators \(H=-Δ_{\mathrm{disc}}+V\) with \(V(n)\to c\in\mathbb…
Strichartz estimate for discrete Schrödinger equation on layered King's grid
Zhiqiang Wan, Heng Zhang
We establish the sharp \( l^1 \to l^{\infty} \) decay estimate for the discrete Schrödinger equation (DS) on the Layered King's Grid (LKG), with a dispersive decay rate of \( \lang…