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.
Categories: hep-th gr-qc math-ph math.AP math.MP