Open AccessModified Korteweg-de Vries equation as a system with benign ghosts
Author(s) -
Andrei Smilga
Publication year - 2022
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/ap.2022.62.0190
Subject(s) - korteweg–de vries equation , mathematical physics , dispersionless equation , dynamics (music) , quantum , physics , classical mechanics , mathematics , kadomtsev–petviashvili equation , mathematical analysis , partial differential equation , quantum mechanics , characteristic equation , nonlinear system , acoustics
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.