Modified Korteweg-de Vries equation as a system with benign ghosts

Andrei Smilga

doi:10.14311/AP.2022.62.0190

Authors

Andrei Smilga University of Nantes, SUBATECH, 4 rue Alfred Kastler, BP 20722, Nantes 44307, France

DOI:

https://doi.org/10.14311/AP.2022.62.0190

Keywords:

benign ghosts, KdV equation, integrability

Abstract

We consider the modified Korteweg-de Vries equation, u_xxx + 6u²u_x + u_t = 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.

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