Modified Korteweg-de Vries Equation as a System with Benign Ghosts (2112.14120v1)

Published 28 Dec 2021 in hep-th, gr-qc, math-ph, math.AP, and math.MP

Abstract: We consider the modified Korteweg-de Vries equation, $ u_{xxx} + 6u² 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.

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Video Overview

Generate a video overview of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

Andrei Smilga

Collections

Sign up for free to add this paper to one or more collections.