Kai Yang

activity

20102026

most citedBlow-up dynamics and spectral property in the

L^{2}

-critical nonlinear Schrödinger equation in high dimensions

20 citations · 88 across the 19 of their papers we have counts for

collaborators

22 papers

math.AP2026

Threshold and Below-Threshold Dynamics for the Energy-Critical NLS: The Higher-Kinetic-Energy Regime

Zuyu Ma, Changxing Miao, Kai Yang +2

We study the focusing energy-critical nonlinear Schrödinger equation below and at the ground-state energy, focusing on solutions in the upper energy cone, characterized by \[ E(u)\…

nlin.PS2026

Robustness of mKdV Breathers: A Numerical Perspective

Chandler Haight, Svetlana Roudenko, Diana Son +1

We systematically investigate breather solutions in the modified Korteweg-de Vries (mKdV) equation via numerical simulations. We show that the breather solutions are stable under a…

math.AP2026

Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential

Zuyu Ma, Yilin Song, Kai Yang +1

We study the threshold scattering problem for the energy-critical nonlinear Schrödinger equation with a repulsive inverse-square potential $\frac{a}{∣ x ∣ ^{2}} > 0$ in dimensions $d= 4…

math.AP2026

The uniqueness of the ground state and the dynamics of nonlinear Schrödinger equation with inverse square potential

Kai Yang, Chongchun Zeng, Xiaoyi Zhang

In this paper, we first provide an alternative proof of the uniqueness of the ground state solution for NLS with inverse square potential and power nonlinearity $∣ u ∣^{p} u$ for all $0…

math.AP2024

Blow-Up Dynamics for the $L^{2}$ critical case of the $2$ D Zakharov-Kuznetsov equation

Francisc Bozgan, Tej-Eddine Ghoul, Nader Masmoudi +1

We study blow-up dynamics for the $L^{2}$ -critical cubic Zakharov--Kuznetsov equation in two dimensions, \[ \partial_tu+\partial_{x_1}(Δu+u^3)=0 \qquad\text{on }\mathbb R^2. \] For a…

math.SP2023

Spectrum of linearized operator at ground states of a system of Klein-Gordon equations

Yan Cui, Bo Xia, Kai Yang

Previously, the existence of ground state solutions of a family of systems of Klein-Gordon equations has been widely studied. In this article, we will study the linearized operator…

math.AP2022★ 8 cited

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

Isaac Friedman, Oscar Riaño, Svetlana Roudenko +2

We consider two types of the generalized Korteweg - de Vries equation, where the nonlinearity is given with or without absolute values, and, in particular, including the low powers…

math.AP2021

On the gap property of a linearized NLS operator

Dong Li, Kai Yang

We consider a pair of linear operators corresponding to the linearization around the ground state soliton of the cubic nonlinear Schrödinger equation in dimension three. We introdu…

math.AP2021

Higher dimensional generalization of the Benjamin-Ono equation: 2D case

Oscar Riaño, Svetlana Roudenko, Kai Yang

We consider a higher-dimensional version of the Benjamin-Ono (HBO) equation in the 2D setting: $u_{t} - R_{1} Δ u + \frac{1}{2} (u^{2})_{x} = 0, (x, y) \in R^{2}$ , which is $L^2…

math.NA2021

Arbitrarily high-order conservative schemes for the generalized Korteweg-de Vries equation

Kai Yang

This paper proposes a new class of arbitrarily high-order conservative numerical schemes for the generalized Korteweg-de Vries (KdV) equation. This approach is based on the scalar…

math.AP2021

Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation

Oussama Landoulsi, Svetlana Roudenko, Kai Yang

We present a numerical study of solutions to the $2 d$ cubic and quintic focusing nonlinear Schrödinger equation in the exterior of a smooth, compact and strictly convex obstacle (a…

math.AP2020★ 14 cited

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

Svetlana Roudenko, Zhongming Wang, Kai Yang

We consider the generalized Benjamin-Ono (gBO) equation on the real line, $u_{t} + \partial_{x} (- H u_{x} + \frac{1}{m} u^{m}) = 0, x \in R, m = 2, 3, 4, 5$ , and perform nu…

math.AP2020★ 2 cited

Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise

Annie Millet, Alex D Rodriguez, Svetlana Roudenko +1

We study the focusing stochastic nonlinear Schrödinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white in time and colored in space, i…

math.AP2020★ 11 cited

Dynamics of threshold solutions for energy critical NLS with inverse square potential

Kai Yang, Chongchun Zeng, Xiaoyi Zhang

We consider the focusing energy critical NLS with inverse square potential in dimension $d = 3, 4, 5$ with the details given in $d = 3$ and remarks on results in other dimensions. Sol…

math.AP2020★ 2 cited

Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation

Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko +1

We consider the quadratic Zakharov-Kuznetsov equation $\partial_{t} u + \partial_{x} Δ u + \partial_{x} u^{2} = 0$ on $R^{3}$ . A solitary wave solution is given by $Q (x - t, y, z)$ , w…

math.AP2020★ 11 cited

Behavior of solutions to the 1D focusing stochastic $L^{2}$ -critical and supercritical nonlinear Schrödinger equation with space-time white noise

Annie Millet, Svetlana Roudenko, Kai Yang

We study the focusing stochastic nonlinear Schrödinger equation in 1D in the $L^{2}$ -critical and supercritical cases with an additive or multiplicative perturbation driven by space-…

math.AP2020★ 2 cited

Stable blow-up dynamics in the $L^{2}$ -critical and $L^{2}$ -supercritical generalized Hartree equation

Kai Yang, Svetlana Roudenko, Yanxiang Zhao

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: $iu_t+Δu +\le…

math.AP2018★ 10 cited

Blow-up in finite or infinite time of the 2D cubic Zakharov-Kuznetsov equation

Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko +1

We prove that near-threshold negative energy solutions to the 2D cubic ( $L^{2}$ -critical) focusing Zakharov-Kuznetsov (ZK) equation blow-up in finite or infinite time. The proof cons…

nlin.AO2018★ 1 cited

Chimera states in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras

Qionglin Dai, Kai Yang, Hongyan Cheng +3

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, prevail in a variety of systems. Here, we consider a population of nonlo…

math.AP2017★ 20 cited

Blow-up dynamics and spectral property in the $L^{2}$ -critical nonlinear Schrödinger equation in high dimensions

Kai Yang, Svetlana Roudenko, Yanxiang Zhao

We study stable blow-up dynamics in the $L^{2}$ -critical nonlinear Schrödinger equation in high dimensions. First, we show that in dimensions $d = 4$ to $d = 12$ generic blow-up behavior…

hep-ph2017★ 7 cited

Cross sections for inelastic meson-meson scattering

Kai Yang, Xiao-Ming Xu, H. J. Weber

We study two kinds of inelastic meson-meson scattering. The first kind is inelastic 2-to-2 meson-meson scattering that is governed by quark interchange as well as quark-antiquark a…

math.CA2010

From Uniform Continuity to Absolute Continuity

Kai Yang, Chenhong Zhu

Absolute continuity implies uniform continuity, but generally not vice versa. In this short note, we present one sufficient condition for a uniformly continuous function to be abso…

Threshold and Below-Threshold Dynamics for the Energy-Critical NLS: The Higher-Kinetic-Energy Regime

Robustness of mKdV Breathers: A Numerical Perspective

Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential

The uniqueness of the ground state and the dynamics of nonlinear Schrödinger equation with inverse square potential

Blow-Up Dynamics for the L2 critical case of the 2D Zakharov-Kuznetsov equation

Spectrum of linearized operator at ground states of a system of Klein-Gordon equations

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

On the gap property of a linearized NLS operator

Higher dimensional generalization of the Benjamin-Ono equation: 2D case

Arbitrarily high-order conservative schemes for the generalized Korteweg-de Vries equation

Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise

Dynamics of threshold solutions for energy critical NLS with inverse square potential

Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation

Behavior of solutions to the 1D focusing stochastic L2-critical and supercritical nonlinear Schrödinger equation with space-time white noise

Stable blow-up dynamics in the L2-critical and L2-supercritical generalized Hartree equation

Blow-up in finite or infinite time of the 2D cubic Zakharov-Kuznetsov equation

Chimera states in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras

Blow-up dynamics and spectral property in the L2-critical nonlinear Schrödinger equation in high dimensions

Cross sections for inelastic meson-meson scattering

From Uniform Continuity to Absolute Continuity

Blow-Up Dynamics for the $L^{2}$ critical case of the $2$ D Zakharov-Kuznetsov equation

Behavior of solutions to the 1D focusing stochastic $L^{2}$ -critical and supercritical nonlinear Schrödinger equation with space-time white noise

Stable blow-up dynamics in the $L^{2}$ -critical and $L^{2}$ -supercritical generalized Hartree equation

Blow-up dynamics and spectral property in the $L^{2}$ -critical nonlinear Schrödinger equation in high dimensions