Physical relation between quantum mechanics and solitons on a thin elastic rod.

Abstract

The 2×2-matrix-valued first-order linear differential equation appears when we solve the modified Korteweg-de Vries (MKdV) equation. This linear differential equation is regarded as a fictitious quantum equation. On the other hand, it is known that the dynamics of an elastic rod is governed by the MKdV equation. In this paper, after we construct a Dirac equation on an elastic rod embedded into (2+1)-dimensional space-time, we show that this linear differential equation is naturally introduced through this Dirac equation