A BILINEAR ESTIMATE WITH APPLICATIONS TO THE KdV EQUATION 1. Introduction In this
article we continue our study of the initial v Page 1 JOURNAL OF THE AMERICAN …

The Korteweg-de Vries equation was first derived by Boussinesq and Korteweg and de
Vries as a model for long-crested small-amplitude long waves propagating on the surface of …

Attention is given to the initial-boundary-value problems (IBVPs) for the Korteweg–de Vries
(KdV) equation and for the Korteweg–de Vries–Burgers (KdV-B) equation. These types of …

The important role of the effects of dispersion on the description of linear and nonlinear
wave motion is well known. Perhaps the most familiar problems in which dispersive effects …

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 …

The article presents solutions for periodic generalized Korteweg-de Vries (KdV) equations.
The problem concerning the local well-posedness for the periodic generalized KdV initial …

Solutions of the Korteweg-deVries Equation with Steplike Initial Data Page 1 JOURNAL OF
DIFFERENTIAL EQUATIONS 63, 306-331 (1986) Solutions of the Korteweg-deVries Equation …

ut -6uux + Ux,, Page 1 SIAM J. MATH. ANAL. Vol. 18, No. July 1987 (C) 1987 Society for
Industrialand Applied Mathematics OO9 SOLUTIONS TO THE KORTEWEG-DE VRIES …

928 KAPPELER Let us point out that the convergence in (3) means that u (x, t) converges to
in H-~(] X,~[) for all x in IR. In particular the theorem can be applied to the case where LI is …

The initial-value problem for the Korteweg-de Vries equation with a forcing term has recently
gained prominence as a model for a number of interesting physical situations. At the same …