Wronskian Representation of the Solutions to the KdV Equation

Abstract

A method to construct solutions to the Korteweg-de-Vries (KdV) equation in terms of wronskians is given. For this, a particular type of polynomials is considered and we obtain for each positive integer n, rational solutions in terms of determinants of order n. Explicit solutions can be easily constructed and rational solutions from order 1 until order 10 are given.