… Korteweg–de Vries modifiée est globalement bien posé dans H1/4(R). Le nouvel ingrédient
… Tao [19] used a homogenous version to prove scattering for generalized KdV equation for …

… Orbital stability of the soliton in the energy space H1 follows from Weinstein’s convexity argument
… of the kink however is closer to the arguments of Martel and Merle for generalised KdV. …

… H solutions of the Cauchy problem for the generalized Kortewegde Vries (KdV) equation … )
Korteweg-de Vries equation, and for a(p)=p2, (1.1’) is the modifiedKorteweg-de Vries equation…

We show well-posedness results for the generalized Korteweg-de Vries equation with
nonlinear term $F(u)\partial_xu$. We assume $F(u)$ is a $C^4$ function and $F(0)=0$. Using a …

… If we consider any combination of two controls (h1 and h2 or h1 and h3), then the system …
(generalized KdV equation) and in [29] the nonlinearity y4yx (critical generalized KdV equation)…

… equation, with corresponding speeds 0 < c1 < c2 < ··· < cN. In this paper, we construct a solution
u(t) of the generalized Korteweg-de Vries equation … result in H1(R): for u0 ∈ H1(R), there …

… In this case, when 8 defines a Hilbert Schmidt operator in H1(R), we are able to generalize
the approach of [17] and to prove global existence and uniqueness of solutions of (1.2), (1.3). …

… of the system described by the Korteweg-de Vries equation … of equations which may be
described as being of Korteweg-de … This again is a generalization of the result known in [15]. …

… limit—the generalized Korteweg–de Vries–Burgers (KdVB) equation. For initial data in H2(R)
we study the notion of viscosity solutions to KdVB, while for the larger H1(R) phase space …

… exist globally in time, but also scatter in the energy norm H1 x(R) to solutions of the Airy
equation (4) as t → +∞ or t → −∞. This essentially follows from the well-posedness theory in …