49 citations · 86 across the 9 of their papers we have counts for
9 papers
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…
Existence and regularity for global solutions including breaking waves from Camassa-Holm and Novikov equations to -family equations
Geng Chen, Yannan Shen, Shihui Zhu
In this paper, we prove the global existence of Hölder continuous solutions for the Cauchy problem of a family of partial differential equations, named as -family equations, whe…
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…
Orbital Stability of Standing Waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions
Tingjian Luo, Shijun Zheng, Shihui Zhu
In this paper, we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrödinger equation with a -Laplacian term (BNLS). Such BNLS models the…
On stability and instability of standing waves for the nonlinear Schrödinger equation with inverse-square potential
Abdelwahab Bensouilah, Van Duong Dinh, Shihui Zhu
We consider the focusing nonlinear Schrödinger equation with inverse square potential \[ i\partial_t u + Δu + c|x|^{-2} u = - |u|^αu, \quad u(0) = u_0 \in H^1, \quad (t,x) \in \mat…
Blow-up for the nonlinear Schrödinger equation with combined nonlinearities
Qing Guo, Shihui Zhu
In the first part of this paper, we investigate the sharp threshold of blow-up and global existence for the focusing nonlinear Schrödinger equation with combined nonlinearities of…
Sharp Criteria of Scattering for the Fractional NLS
Qing Guo, Shihui Zhu
In this paper, the sharp threshold of scattering for the fractional nonlinear Schrödinger equation in the -supercritical case is obtained, i.e., if $1+\frac{4s}{N}<p<1+\frac{4…
Sharp Threshold of Blow-up and Scattering for the fractional Hartree equation
Qing Guo, Shihui Zhu
We consider the fractional Hartree equation in the -supercritical case, and we find a sharp threshold of the scattering versus blow-up dichotomy for radial data: If $ M[u_{0}]…
Existence and Uniqueness of Global Weak solutions of the Camassa-Holm Equation with a Forcing
Shihui Zhu
In this paper, we study the global well-posedness for the Camassa-Holm(C-H) equation with a forcing in by the characteristic method. Due to the forcing, many impo…