6 citations · 8 across the 7 of their papers we have counts for
9 papers
Initial and initial-boundary value problems for a cubic sixth-order Boussinesq equation
Yuhao Xie, Shenghao Li
In this paper, we consider the sixth-order Boussinesq equation with a cubic nonlinearity, \[ u_{tt}-u_{xx}+k u_{xxxx}-u_{xxxxxx}+\left( u^3 \right) _{xx}=0, \ \ \mbox{with }k=\pm 1…
Standing wave solutions of -systems for water waves
Peifei Song, Yuhao Xie, Min Chen +1
We continue the study for standing wave solutions of -systems which was started by Chen and Iooss \cite{chen2005standing} for the BBM system via the Lyapunov-Schmidt method.…
Effect of lower order terms on the well-posedness of Majda-Biello systems
Xin Yang, Shenghao Li, Bing-Yu Zhang
This paper investigates a noteworthy phenomenon within the framework of Majda-Biello systems, wherein the inclusion of lower-order terms can enhance the well-posedness of the syste…
A lower index bilinear estimate for the quadratic Schrödinger equation and application for its half line problem
Shenghao Li, Xin Yang
We prove the local well-posedness of the initial boundary value problem for the nonlinear quadratic Schrödinger equation under low initial-boundary regularity assumption via the bo…
Non-homogeneous boundary value problems for coupled KdV-KdV systems posed on the half line
Shenghao Li, Min Chen, Xin Yang +1
In this article, we study an initial-boundary-value problem of a coupled KdV-KdV system on the half line with non-homogeneous boundary conditions: \begin{equation*…
Lower Regularity Solutions of the Non-homogeneous Boundary-Value Problem for a Higher Order Boussinesq Equation in a Quarter Plane
Shenghao Li, Min Chen, Xin Yang +1
We continue to study the initial-boundary-value problem of the sixth order Boussinesq equation in a quarter plane with non-homogeneous boundary conditions: \begin{equation*} \begin…
Hexagonal standing wave patterns of a two-dimensional Boussinesq system
Shenghao Li, Min Chen, Bing-Yu Zhang
We prove the existence of a large family of two-dimensional standing waves, that are triple periodic solutions, for a Boussinesq system which describes two-way propagation of water…
Exact controllability and stability of the Sixth Order Boussinesq equation
Shenghao Li, Min Chen, Bing-Yu Zhang
The article studies the exact controllability and the stability of the sixth order Boussinesq equation \[ u_{tt}-u_{xx}+βu_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f, \quad β=\pm1, \] on the i…
Lower regularity solutions of non-homogeneous boundary value problems of the sixth order Boussinesq equation in a quarter plane
Shenghao Li, Min Chen, Bingyu Zhang
In this article, we study an initial-boundary-value problem of the sixth order Boussinesq equation on a half line with nonhomogeneous boundary conditions: \[ u_{tt}-u_{xx}+βu_{xxxx…