25 citations · 127 across the 20 of their papers we have counts for
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Local Well-posedness of the Coupled KdV-KdV Systems on
Xin Yang, Bing-Yu Zhang
Inspired by the recent successful completion of the study of the well-posedness theory for the Cauchy problem of the Korteweg-de Vries (KdV) equation \[ u_t +uu_x +u_{xxx}=0, \quad…
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…
Initial boundary value problem for Korteweg-de Vries equation: a review and open problems
Roberto de A. Capistrano-Filho, Shu-Ming Sun, Bing-Yu Zhang
In the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note…