110 citations · 117 across the 8 of their papers we have counts for
8 papers
On the rotation-two-component -family shallow-water system: derivation and wave-breaking analysis
Xingxing Liu
In this paper, we derive the rotation-two-component -family shallow-water wave system from the Green--Naghdi type equations incorporating the effects of the Coriolis force and c…
Two-component system modelling shallow-water waves with constant vorticity under the Camassa-Holm scaling
Leyi Zhang, Xingxing Liu
This paper is concerned with the derivation of a two-component system modelling shallow-water waves with constant vorticity under the Camassa-Holm scaling from our newly establishe…
A new highly nonlinear equation modelling shallow-water waves with constant vorticity
Yu Liu, Xingxing Liu, Min Li
In this paper we apply the approach of formal asymptotic expansions and perturbation theory to derive a new highly nonlinear shallow-water model from the full governing equations f…
Ill-posedness of the Camassa-Holm and related equations in the critical space
Zihua Guo, Xingxing Liu, Luc Molinet +1
We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa-Holm equation, Degasperis-Procesi equation and Novikov equation etc…
Stability of peakons for the generalized modified Camassa-Holm equation
Zihua Guo, Xiaochuan Liu, Xingxing Liu +1
In this paper, we study orbital stability of peakons for the generalized modified Camassa-Holm (gmCH) equation, which is a natural higher-order generalization of the modified Camas…
Stability of the train of solitary waves for the two-component Camassa-Holm shallow water system
Xingxing Liu
Considered herein is the integrable two-component Camassa-Holm shallow water system derived in the context of shallow water theory, which admits blow-up solutions and the solitary…
Stability of peakons for a modified Camassa-Holm equation
Xingxing Liu, Zhaoyang Yin
In this paper, we investigate the orbital stability of peakons for a modified Camassa-Holm equation with cubic nonlinearity derived from the two-dimensional Euler equation. By over…
On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity
Xingxing Liu, Zhijun Qiao, Zhaoyang Yin
In this paper, we study the Cauchy problem for a generalized integrable Camassa-Holm equation with both quadratic and cubic nonlinearity. By overcoming the difficulties caused by t…