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arXiv · 2112.14120

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

Andrei Smilga
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Abstract

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.

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Andrei Smilga. 2021-12-28. Modified Korteweg-de Vries Equation as a System with Benign Ghosts. https://arxiv.org/abs/2112.14120

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