English

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

High Energy Physics - Theory 2021-12-30 v1 General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs math.MP

Abstract

We consider the modified Korteweg-de Vries equation, uxxx+6u2ux+ut = 0 u_{xxx} + 6u^2 u_x + u_t \ =\ 0 , and explore its dynamics in {\it spatial} direction. Higher xx 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.

Keywords

Cite

@article{arxiv.2112.14120,
  title  = {Modified Korteweg-de Vries Equation as a System with Benign Ghosts},
  author = {Andrei Smilga},
  journal= {arXiv preprint arXiv:2112.14120},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-24T08:33:36.304Z