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


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



benign ghosts, KdV equation, integrability


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.


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Analytic and Algebraic Methods in Physics