Coherent States and the Korteweg-de Vries Equation for a System of Interacting Phonons

Abstract

The Korteweg-de Vries equation for a system of interacting phonons is derived on the basis of the coherent state representation of phonons in a one-dimensional anharmonic lattice. A soliton solution of the Korteweg-de Vries equation can be given quantum mechanical interpretation as the coherent state in which a large number of phonons are excited in accord with a Poisson distribution.