We prove a full asymptotic stability result for solitary wave solutions of the mKdV equation.
We consider small perturbations of solitary waves with polynomial decay at infinity and …

This paper describes the interaction of two solitons with nearly equal speeds for the quartic
(gKdV) equation 0.1\partial_tu+\partial_x (\partial_x^ 2u+ u^ 4)= 0,\quad t, x ∈ R. We call …

In this paper, we investigate the pointwise convergence problem of the generalized
Korteweg-de Vries (gKdV) equation with data in the Fourier-Lebesgue space. Firstly, for the …

In this paper our first aim is to identify a large class of non-linear functions f (·) for which the
IVP for the generalized Korteweg–de Vries equation does not have breathers or “small” …

In this article, we prove the existence of a non-scattering solution, which is minimal in some
sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale …

The Cauchy problem for the generalized Zakharov-Kuznetsov equation $$\partial_t
u+\partial_x\Delta u=\partial_x u^{k+ 1},\qquad\qquad u (0)= u_0 $$ is considered in space …

We construct the “threshold manifold” near the soliton for the mass critical gKdV equation,
completing results obtained in Martel et al.(Acta Math 212: 59–140, 2014, J Math Eur Soc …

We consider the generalized Korteweg-de Vries (gKdV) equation $\partial_t u+\partial_x^
3u+\mu\partial_x (u^{k+ 1})= 0$, where $ k\geq5 $ is an integer number and $\mu=\pm1 $. In …

In this paper, we give an improvement of nondiagonal Strichartz estimates for the Airy
equation by using a Morrey-type space. As its applications, we prove the small data …

The purpose of this paper is to study local and global well-posedness of the initial value
problem for the generalized Korteweg–de Vries (gKdV) equation in L ̂ r={f∈ S′(ℝ):∥ f∥ L …