Modified Korteweg-de Vries equation as a system with benign ghosts

Abstract

We consider the modified Korteweg-de Vries equation, uxxx + 6u2ux + ut = 0, and explore its dynamics in spatial direction. Higher x derivatives bring about the ghosts. We argue that these ghosts are benign, i.e., the classical dynamics of this system does not involve a blow-up. This probably means that the associated quantum problem is also well defined.