We calculate infinite set of initial profiles of higher integer Korteweg-de Vries (KdV) solitons, which are both exactly solvable for the Schrödinger 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.
- Darboux transformation
- KdV equation
- Multi-indexed extensions of soliton potential