Concepedia

A bilinear estimate with applications to the KdV equation

Carlos E. Kenig, Gustavo Ponce, Luis Vega

Journal of the American Mathematical Society · 1996 · 864 citations · 32 references

DOIFull text

Open access

Concepts

Abstract

In this article we continue our study of the initial value problem (IVP) for the Korteweg-de Vries (KdV) equation with data in the classical Sobolev space Hs(R). Thus we consider

References

32

Method for Solving the Korteweg-deVries Equation

Clifford S. Gardner, J. M. Greene, Martin D. Kruskal et al. · Physical Review Letters · 1967 · 4.6K citations

, , +17

XLI. <i>On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves</i>

D. J. Korteweg, G. de Vries · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · 1895 · 4.1K citations

, , +5

Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations

Jean Bourgain · Geometric and Functional Analysis · 1993 · 1.7K citations

, , +9

Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle

Carlos E. Kenig, Gustavo Ponce, Luis Vega · Communications on Pure and Applied Mathematics · 1993 · 1.4K citations

, , +14

Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations

Robert S. Strichartz · Duke Mathematical Journal · 1977 · 1.3K citations

, , +16