Multi-indexed extensions of soliton potential and extended integer solitons of KdV equation

Abstract

We calculate infinite set of initial profiles of higher integer Korteweg-de Vries (KdV) solitons, which are both exactly solvable for the Schrodinger equation and for the Gel\'fand-Levitan-Marchenko (GLM) equation in the inverse scattering transform (IST) method of KdV equation. The calculation of these higher integer soliton solutions is based on the recently developed multi-indexed extensions of the reflectionless soliton potential.