For s>1 two sequences of CH solutions living in a bounded subset of the Sobolev space
H^s(R) are constructed, whose distance at the initial time is converging to zero while at any …

This work studies the initial value problem (ivp) for a generalized Camassa-Holm equation
with (k+1)-order nonlinearities (gk bCH) and containing, as its members, three integrable …

It is shown that the initial value problem for the Fokas–Olver–Rosenau–Qiao equation
(FORQ) is well-posed in Sobolev spaces H s, s> 5/2, in the sense of Hadamard …

We solve the open problem of spectral stability of smooth periodic waves in the Camassa–
Holm equation. The key to obtaining this result is that the periodic waves of the Camassa …

It is shown in both the periodic and the non-periodic cases that the data-to-solution map for
the Degasperis-Procesi (DP) equation is not a uniformly continuous map on bounded …

Peaked periodic waves in the Camassa--Holm equation are revisited. Linearized evolution
equations are derived for perturbations to the peaked periodic waves, and linearized …

In this paper, we prove well-posedness of the Fornberg–Whitham equation in Besov spaces
B 2, rs in both the periodic and non-periodic cases. This will imply the existence and …

For the Novikov equation, on both the line and the circle, we construct a 2-peakon solution
with an asymmetric antipeakon-peakon initial profile whose H^s-norm for s<3/2 is arbitrarily …

This work presents an Ovsyannikov type theorem for an autonomous abstract Cauchy
problem in a scale of decreasing Banach spaces, which in addition to existence and …

In this paper, we show that the Fornberg–Whitham equation is Well-posed in Sobolev
spaces H s, for s> 3/2, and in the periodic case. We then show that the Well-posedness is …