22 citations · 41 across the 9 of their papers we have counts for
9 papers
The monotonicity conjecture and stability of solitons for the Cubic-Quintic NLS on R^3
Jian Zhang, Shuihui Zhu
In this paper, we prove stability or instability of solitons for the cubic-quintic nonlinear Schrodinger equation at every frequency. The monotonicity conjecture raised by Killip,…
Stability of Big Solitons in a Competitive Power Nonlinear Schrödinger Equation
Jian Zhang, Mengxue Bai
By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinea…
Small Solitons and Multi-Solitons in Generalized Davey-Stewartson System
Mengxue Bai, Jian Zhang, Shihui Zhu
This paper is concerned with the generalized Davey-Stewarston system in two dimensional space. Existence and stability of small solitons are proved by solving two correlative const…
Orbital Stability of Standing Waves for Fractional Hartree Equation with Unbounded Potentials
Jian Zhang, Shijun Zheng, Shihui Zhu
We prove the existence of the set of ground states in a suitable energy space , for the ma…
Multiplicity and concentration behavior of solutions to the critical Kirchhoff type problem
Jian Zhang, Wenming Zou
In this paper, we study the multiplicity and concentration of the positive solutions to the following critical Kirchhoff type problem: \begin{equation*} -\left(\varepsilon^2 a+\var…
Slow foliation of a slow-fast stochastic evolutionary system
Guanggan Chen, Jinqiao Duan, Jian Zhang
This work is concerned with the dynamics of a slow-fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geo…
Approximating dynamics of a singularly perturbed stochastic wave equation with a random dynamical boundary condition
Guanggan Chen, Jinqiao Duan, Jian Zhang
This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximat…
Effective dynamics of stochastic wave equation with a random dynamical boundary condition
Guanggan Chen, Jinqiao Duan, Jian Zhang
This work is devoted to the effective macroscopic dynamics of a weakly damped stochastic nonlinear wave equation with a random dynamical boundary condition. The white noises are ta…
Geometric shape of invariant manifolds for a class of stochastic partial differential equations
Guanggan Chen, Jinqiao Duan, Jian Zhang
Invariant manifolds play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. However, the geometric shape…