Modified Korteweg-de Vries Equation as a System with Benign Ghosts

Abstract

We consider the modified Korteweg-de Vries equation, $u_{xxx}+6u^2{u}_x+u_t=0$, and explore its dynamics in {\it spatial} direction. Higher $x$ derivatives bring about the {\it 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 also the associated quantum problem is well defined.

16 pages, 6 figures. A talk given at the AAMP conference, Prague, September 2021