New Representations of the Soliton Solution for the Korteweg-de Vries Equation

Abstract

A method of solution for the Korteweg-de Vries equation is presented. It is shown that the N-soliton solution is expressed in a compact form using a trace of matrix. It is also shown that a field theoretical representation is possible for the N-soliton solution. The representation yields a novel derivation of the Gelfand-Levitan equation.