Of concern is the study of fractional order Sobolev-type metrics on the group of H∞-
diffeomorphism of R d and on its Sobolev completions D q (R d). It is shown that the H s …

In this manuscript, we study the well-posedness, blow-up scenario and global solution of a
two–component b–family equations in space H s-1, p (R)× H s, p (R), s> max {2, 3 2+ 1 p} …

In this paper, we consider a simple equation which involves a parameter k, and its traveling
wave system has a singular line. Firstly, using the qualitative theory of differential equations …

We present some geometric investigations on some recently derived shallow water
equations. While the Camassa–Holm equation can be expressed as an Euler equation on …

On the Cauchy problem for a two-component b-family system - ScienceDirect Skip to main
contentSkip to article Elsevier logo Journals & Books Search RegisterSign in View PDF …

In this paper, we study the Cauchy problem of a two-component b-family system. We first
establish the local well-posedness for a two-component b-family system by Kato's …

In this paper, we mainly revisit a weakly dissipative periodic two‐component bb‐family
system. Considering the dissipative effect, the local well‐posedness is first obtained for the …

We develop a theory of Lagrangian reduction on loop groups for completely integrable
systems after having exchanged the role of the space and time variables in the multi-time …

In this paper, the method of bifurcation of planar dynamic systems is used to investigate
bounded traveling wave solutions for the two-component Degasperis–Procesi shallow water …

In this article, we investigate some new asymptotic behaviors of the solution for a two-
component b-family equations. We first prove the persistence properties of the solution for …