Application of the Trace Method to the Modified Korteweg-de Vries Equation

Abstract

The trace method which has been proposed in a recent paper by the authors is applied to the modified Korteweg-de Vries equation. It is shown that the N-soliton solution is put into a compact form using a trace of matrix. It is also shown that a field theoretical representation for the N-soliton solution yields a simple derivation of the Gelfand-Levitan equation.