Bracken, Paul - In: Physica A: Statistical Mechanics and its Applications 335 (2004) 1, pp. 70-78
The constraint equation which must hold for the reciprocal of a known solution for the Korteweg–de Vries (KdV) equation to be a solution itself is derived. These reciprocal solutions are required to satisfy a differential equation which is in fact a Painlevé equation. A differential...