Cheng Zhang

activity

20142026

most citedImproved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature

12 citations · 63 across the 29 of their papers we have counts for

collaborators

29 papers

math.CA2026

Eigenvalues and eigenfunctions of the fractional Laplacian on the interval

Cheng Zhang

We prove a three-term asymptotic formula for the eigenvalues of the fractional Laplacian on the bounded interval $(- 1, 1)$ . This improves the eigenvalue asymptotics of Kulczycki--Kw…

math.AP2026

Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters

Shengwen Gan, Cheng Zhang, Zhifei Zhu

We prove sharp $k$ -linear $L^{p}$ estimates for Carleson--Sjölin oscillatory integral operators with arbitrary separated frequency scales for all $k \geq 2$ and $1 \leq p \leq \infty$ . The…

math.AP2026

Restriction estimates for toral eigenfunctions and lattice points in spherical regions

Cheng Zhang, Zhifei Zhu

We establish new $L^{2}$ restriction estimates for toral eigenfunctions. These estimates are sharp in certain cases, and thus prove a conjecture of Huang-Zhang for smooth submanifold…

math.AG2026

A numerical generalized canonical bundle formula

Cheng Zhang

We establish the generalized canonical bundle formula in the numerical setting.

math.CA2026

Maximal growth of the Stein-Wainger oscillatory integral

Cheng Zhang, Zhifei Zhu

We determine the optimal growth of the Stein--Wainger oscillatory integral for every Denjoy--Carleman class defined by a positive log-convex sequence. Quasianalyticity is equivalen…

math.AP2023

Sharp local $L^{p}$ estimates for the Hermite eigenfunctions

Xing Wang, Cheng Zhang

We investigate the concentration of eigenfunctions for the Hermite operator $H = - Δ + ∣ x ∣^{2}$ in $R^{n}$ by establishing local $L^{p}$ bounds over the compact sets with arbitrary d…

math.AP2022

Sharp $L^{p}$ estimates and size of nodal sets for generalized Steklov eigenfunctions

Xiaoqi Huang, Yannick Sire, Xing Wang +1

We prove sharp $L^{p}$ estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their $L^{2}$ norms on the boundary. We prove it by establishing $L^{p}$ bo…

nlin.SI2022★ 5 cited

Nonlinear Schrödinger equation on the half-line without a conserved number of solitons

Vincent Caudrelier, Nicolas Crampe, Eric Ragoucy +1

We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schrödinger equation on the half-line. This is based on the investigation of…

nlin.SI2021

Classification of integrable boundary equations for integrable quad-graph systems

Pengyu Sun, Cheng Zhang

In the context of integrable systems on quad-graphs, the boundary consistency around a half of a rhombic dodecahedron, as a companion notion to the three-dimensional consistency ar…

math.AP2021★ 3 cited

Sharp Pointwise Weyl Laws for Schrödinger Operators with Singular Potentials on Flat Tori

Xiaoqi Huang, Cheng Zhang

The Weyl law of the Laplacian on the flat torus $T^{n}$ is concerning the number of eigenvalues $\leq λ^{2}$ , which is equivalent to counting the lattice points inside the ball…

nlin.SI2021★ 3 cited

On an inverse scattering transform for the nonlinear Schödinger equation on the half-line

Cheng Zhang

In this paper, we develop an inverse scattering transform for the integrable focusing nonlinear Schrödinger (NLS) equation on the half-line subject to a class of boundary condition…

math.AP2021

Pointwise Weyl Laws for Schrödinger operators with singular potentials

Xiaoqi Huang, Cheng Zhang

We consider the Schrödinger operators $H_{V} = - Δ_{g} + V$ with singular potentials $V$ on general $n$ -dimensional Riemannian manifolds and study whether various forms of pointwise Weyl la…

math-ph2020★ 3 cited

Integrable boundary conditions for quad equations, open boundary reductions and integrable mappings

Vincent Caudrelier, Peter H. van der Kamp, Cheng Zhang

In the context of integrable partial difference equations on quad-graphs, we introduce the notion of open boundary reductions as a new means to construct discrete integrable mappin…

math.AP2020

$L^{p}$ eigenfunction bounds for fractional Schrödinger operators on manifolds

Xiaoqi Huang, Yannick Sire, Cheng Zhang

This paper is dedicated to $L^{p}$ bounds on eigenfunctions of a Schödinger-type operator $(- Δ_{g})^{α /2} + V$ on closed Riemannian manifolds for critically singular potentials $V$ . The…

nlin.SI2020

Eigenfunction equations of lattice KdV equations and connections to ABS lattice equations with a $δ$ term

Cheng Zhang, Haifei Zhang, Da-jun Zhang

We develop lattice eigenfunction equations of lattice KdV equation, which are equations obeyed by the auxiliary functions, or eigenfunctions, of the Lax pair of the lattice KdV equ…

math.AP2019★ 2 cited

Interior estimates for the eigenfunctions of the fractional Laplacian on a bounded Euclidean domain

Xiaoqi Huang, Yannick Sire, Cheng Zhang

This paper is devoted to interior, i.e. away from the boundary, estimates for eigenfunctions of the fractional Laplacian in an Euclidean domain of $R^{d}$ .

nlin.SI2019★ 1 cited

Squared eigenfunction symmetry of the D $Δ$ mKP hierarchy and its constraint

Kui Chen, Cheng Zhang, Da-jun Zhang

In this paper squared eigenfunction symmetry of the differential-difference modified Kadomtsev-Petviashvili (D $Δ$ mKP) hierarchy and its constraint are considered. Under the constra…

nlin.SI2019★ 1 cited

Vector NLS solitons interacting with a boundary

Cheng Zhang, Da-jun Zhang

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the h…

math.AP2019★ 7 cited

Restriction of toral eigenfunctions to totally geodesic submanifolds

Xiaoqi Huang, Cheng Zhang

We estimate the $L^{2}$ norm of the restriction to a totally geodesic submanifold of the eigenfunctions of the Laplace-Beltrami operator on the standard flat torus $T^{d}$ , $d…

nlin.SI2018★ 1 cited

Dressing the boundary: on soliton solutions of the nonlinear Schrödinger equation on the half-line

Cheng Zhang

Based on the theory of integrable boundary conditions (BCs) developed by Sklyanin, we provide a direct method for computing soliton solutions of the focusing nonlinear Schrödinger…

nlin.SI2018★ 5 cited

Dressing the Dressing Chain

Charalampos A. Evripidou, Peter H. van der Kamp, Cheng Zhang

The dressing chain is derived by applying Darboux transformations to the spectral problem of the Korteweg-de Vries (KdV) equation. It is also an auto-Bäcklund transformation for th…

nlin.SI2018★ 4 cited

Discrete Crum's Theorems and Integrable Lattice Equations

Cheng Zhang, Linyu Peng, Da-jun Zhang

In this paper, we develop discrete versions of Darboux transformations and Crum's theorems for two second order difference equations. The difference equations are discretised versi…

math.CA2017★ 1 cited

Zeros of the deformed exponential function

Liuquan Wang, Cheng Zhang

Let $f (x) = \sum_{n = 0}^{\infty} \frac{1}{n !} q^{n (n - 1) /2} x^{n}$ ( $0 < q < 1$ ) be the deformed exponential function. It is known that the zeros of $f (x)$ are real and form a negative decreasi…

math.AP2016★ 1 cited

An Endpoint Version of Uniform Sobolev Inequalities

Tianyi Ren, Yakun Xi, Cheng Zhang

We prove an endpoint version of the uniform Sobolev inequalities in Kenig-Ruiz-Sogge [8]. It was known that strong type inequalities no longer hold at the endpoints; however, we sh…

Eigenvalues and eigenfunctions of the fractional Laplacian on the interval

Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters

Restriction estimates for toral eigenfunctions and lattice points in spherical regions

A numerical generalized canonical bundle formula

Maximal growth of the Stein-Wainger oscillatory integral

Sharp local Lp estimates for the Hermite eigenfunctions

Sharp Lp estimates and size of nodal sets for generalized Steklov eigenfunctions

Nonlinear Schrödinger equation on the half-line without a conserved number of solitons

Classification of integrable boundary equations for integrable quad-graph systems

Sharp Pointwise Weyl Laws for Schrödinger Operators with Singular Potentials on Flat Tori

On an inverse scattering transform for the nonlinear Schödinger equation on the half-line

Pointwise Weyl Laws for Schrödinger operators with singular potentials

Integrable boundary conditions for quad equations, open boundary reductions and integrable mappings

Lp eigenfunction bounds for fractional Schrödinger operators on manifolds

Eigenfunction equations of lattice KdV equations and connections to ABS lattice equations with a δ term

Interior estimates for the eigenfunctions of the fractional Laplacian on a bounded Euclidean domain

Squared eigenfunction symmetry of the DΔmKP hierarchy and its constraint

Vector NLS solitons interacting with a boundary

Restriction of toral eigenfunctions to totally geodesic submanifolds

Dressing the boundary: on soliton solutions of the nonlinear Schrödinger equation on the half-line

Dressing the Dressing Chain

Discrete Crum's Theorems and Integrable Lattice Equations

Zeros of the deformed exponential function

An Endpoint Version of Uniform Sobolev Inequalities

Sharp local $L^{p}$ estimates for the Hermite eigenfunctions

Sharp $L^{p}$ estimates and size of nodal sets for generalized Steklov eigenfunctions

$L^{p}$ eigenfunction bounds for fractional Schrödinger operators on manifolds

Eigenfunction equations of lattice KdV equations and connections to ABS lattice equations with a $δ$ term

Squared eigenfunction symmetry of the D $Δ$ mKP hierarchy and its constraint