It has been shown that the Cauchy problem for the Fokas–Olver–Rosenau–Qiao equation is
well-posed for initial data u_0 ∈ H^ su 0∈ H s, s> 5/2 s> 5/2, with its data-to-solution map …

The Novikov equation (NE) has been discovered recently as a new integrable equation with
cubic nonlinearities that is similar to the Camassa-Holm and Degasperis-Procesi equations …

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 …

Considered herein is the initial value problem for the two-component Novikov system with
peakons. Based on the local well-posedness results for this problem, it is shown that the …

It is shown that the data-to-solution map for the generalized reduced Ostrovsky (gRO)
equation is not uniformly continuous on bounded sets in Sobolev spaces on the circle with …

For Sobolev exponents greater than 3/2, it is proved that the data-to-solution map for the b-
family equation is continuous from H^s(T) into C(0,T;H^s(T)) but not uniformly continuous …

Abstract For Sobolev exponent s>3/2, it is shown that the data-to-solution map for the 2-
component Camassa--Holm system is continuous from H^s*H^s-1(T) into C(0,T;H^s*H^s …

This work studies the Cauchy problem of a two-component higher order Camassa–Holm
system, which is well-posed in Sobolev spaces H s (R)× H s− 2 (R), s> 7 2 and its solution …

This work studies a generalized Camassa–Holm equation with higher order nonlinearities (g-
kbCH). The Camassa–Holm, the Degasperis–Procesi and the Novikov equations are …

Considered herein is the Cauchy problem for the four-component Novikov system with
peakon solutions on the line. At first, we establish the result with respect to the non-uniform …