相关论文: On the Cauchy problem for a generalized Camassa-Ho…
This paper investigates the Cauchy problem of a generalized Camassa-Holm equation with quadratic and cubic nonlinearities (alias the mCH-Novikov-CH equation), which is a generalization of some special equations such as the Camassa-Holm (CH)…
In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local…
Considered in this paper is the modified Camassa-Holm equation with cubic nonlinearity, which is integrable and admits the single peaked solitons and multi-peakon solutions. The short-wave limit of this equation is known as the short-pulse…
Consideration here is a generalized $\mu$-type integrable equation, which can be regarded as a generalization to both the $\mu$-Camassa-Holm and modified $\mu$-Camassa-Holm equations. It is shown that the proposed equation is formally…
In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the…
This paper is devoted to an integrable two-component Camassa-Holm system with cubic nonlinearity, which includes the cubic Camassa-Holm equation (also called the Fokas-Olver-Rosenau-Qiao equation) as a special case. The one peaked solitons…
In this paper, we study the Cauchy problem for a generalized cross-coupled Camassa-Holm system with peakons and higher-order nonlinearities. By the transport equation theory and the classical Friedrichs regularization method, we obtain the…
This paper is devoted to the Cauchy problem for the modified multi-component Camassa-Holm system in higher dimensions. On the one hand, we establish an almost complete local well-posedness results for the system in the framework of Besov…
In this paper, we consider the Cauchy problem for a class of weakly dissipative Camassa-Holm equations in nonhomogeneous Besov spaces. First, we prove that the Cauchy problem admits a unique global strong solution in Besov spaces with…
In this paper, we study the following generalized Camassa-Holm equation with both cubic and quadratic nonlinearities: $$ m_{t}+k_{1}(3uu_{x}m+u^2m_{x})+k_{2}(2mu_{x}+m_{x}u)=0, \quad m=u-u_{xx}, $$ which is presented as a linear combination…
In this paper we mainly investigate the Cauchy problem of a generalized Camassa-Holm equation. First by this relationship between the Degasperis-Procesi equation and the generalized Camassa-Holm equation, we then obtain two global…
In this paper, we mainly consider the Cauchy problem of a weakly dissipative Camassa-Holm equation. We first establish the local well-posedness of equation in Besov spaces $B^{s}_{p,r}$ with $s>1+\frac 1 p$ and $s=1+\frac 1 p , r=1,p\in…
In this paper, we study the Cauchy problem of a higher-order $\mu$-Camassa-Holm equation. We first establish the Green's function of $(\mu-\partial_{x}^{2}+\partial_{x}^{4})^{-1}$ and local well-posedness for the equation in Sobolev spaces…
In this letter, we propose a (2+1)-dimensional generalized Camassa-Holm (2dgCH) hierarchy with both quadratic and cubic nonlinearity. The Lax representation and peakon solutions for the 2dgCH system are derived.
This paper is contributed to study the Cauchy problem of a new integrable two-component system with peaked soliton (peakon) and weak kink solutions. We first establish the local well-posedness result for the Cauchy problem in Besov spaces,…
In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation that includes the Camassa-Holm as well as the Novikov equation on the line. We present a new and unified method to prove the sharp ill-posedness for the…
In this paper, we propose a three-component Camassa-Holm (3CH) system with cubic nonlinearity and peakons. The 3CH model is proven integrable in the sense of Lax pair, Hamiltonian structure, and conservation laws. We show that this system…
In this paper we mainly investigate the Cauchy problem of a three-component Camassa-Holm system. By using the method of approximation of smooth solutions, a regularization technique and the special structure of the system, we prove the…
A nonlinearly generalized Camassa-Holm equation, depending an arbitrary nonlinearity power $p \neq 0$, is considered. This equation reduces to the Camassa-Holm equation when $p=1$ and shares one of the Hamiltonian structures of the…
In this paper, we investigate the orbital stability problem of peakons for a modified Camassa-Holm equation with both quadratic and cubic nonlinearity. This equation was derived from integrable theory and admits peaked soliton (peakon) and…