A new two-component system with cubic nonlinearity and linear dispersion: mt= bux+ 1 2 [m
(uv− uxvx)] x− 1 2 m (uvx− uxv), nt= bvx+ 1 2 [n (uv− uxvx)] x+ 1 2 n (uvx− uxv), m= u− uxx …

In this paper, we deal with the Cauchy problem for a generalized two-component Camassa-
Holm system with waltzing peakons and complex higher-order nonlinear terms. By the …

This paper deals with the Cauchy problem for a cross-coupled Camassa–Holm equation
m_t=-(vm) _x-mv_x, n_t=-(un) _x-nu_x, mt=-(vm) x-mvx, nt=-(un) x-nux, where n ≐ v-v_ xx n≐ …

The geodesic equations of a class of right invariant metrics on the semi-direct product Diff (S
1) sDiff (S 1) are studied. The equations are explicitly described, they have the form of a …

In this paper we examine the evolution of solutions, of a recently-derived system of cross-
coupled Camassa-Holm equations, that initially have compact support. The analytical …

We consider a Lax pair found by Xia, Qiao and Zhou for a family of two-component
analogues of the Camassa-Holm equation, including an arbitrary function $ H $, and show …

In this paper, we consider the well-posedness problem in the sense of Hadamard, non-
uniform dependence, and Hölder continuity of the data-to-solution map for a generalized …

In this paper, we consider a generalized two component Camassa-Holm system. Based on
local well-posedness results and lifespan estimates, we establish sharpness of continuity on …

By requiring B= P∧ s T∧ d A and substituting u= A+ B into the b‐family equation and
Novikov equation, we can obtain Alice‐Bob peakon systems, where P∧ s and T∧ d are the …

In this paper, we mainly study the well-posedness in the sense of Hadamard, non-uniform
dependence, Hölder continuity and analyticity of the data-to-solution map for a cross …