… This work studies the initial value problem (ivp) for a generalized Camassa-Holm equation
… integrable equations: the Camassa-Holm, the Degasperis-Procesi and the Novikov equations…

… In this paper, we consider the Cauchy problem of the generalized Camassa–Holm equation
in both the periodic and the nonperiodic case, respectively.(1.1) u t − u t x x = ∂ x ( 2 − ∂ x ) …

… equation do not depend uniformly continuously on the initial data in H s ( R ) with s < 3 / 2 …
, we show that the Cauchy problem for the generalized Camassa–Holm equation is locally well-…

… In this paper, we are concerned with the Cauchy problem of the generalized Camassa–Holm
equation, which was proposed by Hakkaev and Kirchev (Comm Part Diff Equ 30:761–781, …

… of the generalized Camassa-Holm equation … generalized Camassa-Holm equation with
initial data , respectively. We will prove (3.39) Obviously, satisfies the following transport equation …

… Kato's theorem is known to hold under more general hypothesis [12]. However, we
preferred to state this result with less general (and slightly modified) assumptions, because it is …

… Camassa–Holm equation after wave breaking. By introducing a new set of independent and
dependent variables, the evolution problem is … condition, the Cauchy problem has a unique …

… We study the periodic Cauchy problem for the Camassa–Holm equation and prove that it
is locally well-posed in the space of continuously differentiable functions on the circle. The …

… This paper deals with the Cauchy problem for the modified Camassa-Holm (mCH) equation
… -breaking mechanisms for the mCH equation and its generalizations, particularly, the mCH …

… Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits,
… Misiołek, The Cauchy problem for an integrable shallow-water equation, Differential Integral …