Unique continuation principle for high order equations of Korteweg-de Vries type

Abstract

In this article we consider the problem of unique continuation for high-order equations of Korteweg-de Vries type which include the kdV hierarchy. It is proved that if the difference w of two solutions of an equation of this form has certain exponential decay for x >0 at two different times, then w is identically zero.

Keywords

• Nonlinear dispersive equations
• unique continuation
• estimates of Carleman type